Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations

Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations book. This book definitely worth reading, it is an incredibly well-written.

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

N. V. Krylov
Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations Book PDF

Author : N. V. Krylov
Publisher : American Mathematical Soc.
Page : 441 pages
File Size : 46,7 Mb
Release : 2018-09-07
Category : Differential equations, Parabolic
ISBN : 9781470447403

Get Book

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations by N. V. Krylov Pdf

This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞

Nikos Katzourakis
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L Book PDF

Author : Nikos Katzourakis
Publisher : Springer
Page : 123 pages
File Size : 41,7 Mb
Release : 2014-11-26
Category : Mathematics
ISBN : 9783319128290

Get Book

An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ by Nikos Katzourakis Pdf

The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.

Nonlinear Elliptic and Parabolic Equations of the Second Order

N.V. Krylov
Nonlinear Elliptic and Parabolic Equations of the Second Order Book PDF

Author : N.V. Krylov
Publisher : Springer
Page : 0 pages
File Size : 54,8 Mb
Release : 2001-11-30
Category : Mathematics
ISBN : 140200334X

Get Book

Nonlinear Elliptic and Parabolic Equations of the Second Order by N.V. Krylov Pdf

Approach your problems from the It isn't that they can't see the right end and begin with the solution. It is that they can't see answers. Then one day, perhaps the problem. you will find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theor.etical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Fully Nonlinear Elliptic Equations

Luis A. Caffarelli,Xavier Cabré
Fully Nonlinear Elliptic Equations Book PDF

Author : Luis A. Caffarelli,Xavier Cabré
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 49,5 Mb
Release : 1995
Category : Mathematics
ISBN : 0821804375

Get Book

Fully Nonlinear Elliptic Equations by Luis A. Caffarelli,Xavier Cabré Pdf

The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.

Linear and Quasilinear Parabolic Systems: Sobolev Space Theory

David Hoff
Linear and Quasilinear Parabolic Systems Sobolev Space Theory Book PDF

Author : David Hoff
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 45,9 Mb
Release : 2020-11-18
Category : Education
ISBN : 9781470461614

Get Book

Linear and Quasilinear Parabolic Systems: Sobolev Space Theory by David Hoff Pdf

This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.

Maximal Function Methods for Sobolev Spaces

Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Maximal Function Methods for Sobolev Spaces Book PDF

Author : Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 40,7 Mb
Release : 2021-08-02
Category : Education
ISBN : 9781470465759

Get Book

Maximal Function Methods for Sobolev Spaces by Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas Pdf

This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.

Analysis of Monge–Ampère Equations

Nam Q. Le
Analysis of Monge Amp re Equations Book PDF

Author : Nam Q. Le
Publisher : American Mathematical Society
Page : 599 pages
File Size : 44,7 Mb
Release : 2024-03-07
Category : Mathematics
ISBN : 9781470474201

Get Book

Analysis of Monge–Ampère Equations by Nam Q. Le Pdf

This book presents a systematic analysis of the Monge–Ampère equation, the linearized Monge–Ampère equation, and their applications, with emphasis on both interior and boundary theories. Starting from scratch, it gives an extensive survey of fundamental results, essential techniques, and intriguing phenomena in the solvability, geometry, and regularity of Monge–Ampère equations. It describes in depth diverse applications arising in geometry, fluid mechanics, meteorology, economics, and the calculus of variations. The modern treatment of boundary behaviors of solutions to Monge–Ampère equations, a very important topic of the theory, is thoroughly discussed. The book synthesizes many important recent advances, including Savin's boundary localization theorem, spectral theory, and interior and boundary regularity in Sobolev and Hölder spaces with optimal assumptions. It highlights geometric aspects of the theory and connections with adjacent research areas. This self-contained book provides the necessary background and techniques in convex geometry, real analysis, and partial differential equations, presents detailed proofs of all theorems, explains subtle constructions, and includes well over a hundred exercises. It can serve as an accessible text for graduate students as well as researchers interested in this subject.

Computational Management

Srikanta Patnaik,Kayhan Tajeddini,Vipul Jain
Computational Management Book PDF

Author : Srikanta Patnaik,Kayhan Tajeddini,Vipul Jain
Publisher : Springer Nature
Page : 682 pages
File Size : 52,6 Mb
Release : 2021-05-29
Category : Technology & Engineering
ISBN : 9783030729295

Get Book

Computational Management by Srikanta Patnaik,Kayhan Tajeddini,Vipul Jain Pdf

This book offers a timely review of cutting-edge applications of computational intelligence to business management and financial analysis. It covers a wide range of intelligent and optimization techniques, reporting in detail on their application to real-world problems relating to portfolio management and demand forecasting, decision making, knowledge acquisition, and supply chain scheduling and management.

Comparison Principles for General Potential Theories and PDEs

Marco Cirant,F. Reese Harvey,H. Blaine Lawson,Kevin R. Payne
Comparison Principles for General Potential Theories and PDEs Book PDF

Author : Marco Cirant,F. Reese Harvey,H. Blaine Lawson,Kevin R. Payne
Publisher : Princeton University Press
Page : 224 pages
File Size : 53,7 Mb
Release : 2023-10-03
Category : Mathematics
ISBN : 9780691243627

Get Book

Comparison Principles for General Potential Theories and PDEs by Marco Cirant,F. Reese Harvey,H. Blaine Lawson,Kevin R. Payne Pdf

An examination of the symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories In recent years, there has evolved a symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories. This book examines important aspects of this story. One main purpose is to prove comparison principles for nonlinear potential theories in Euclidian spaces straightforwardly from duality and monotonicity under the weakest possible notion of ellipticity. The book also shows how to deduce comparison principles for nonlinear differential operators, by marrying these two points of view, under the correspondence principle. The authors explain that comparison principles are fundamental in both contexts, since they imply uniqueness for the Dirichlet problem. When combined with appropriate boundary geometries, yielding suitable barrier functions, they also give existence by Perron’s method. There are many opportunities for cross-fertilization and synergy. In potential theory, one is given a constraint set of 2-jets that determines its subharmonic functions. The constraint set also determines a family of compatible differential operators. Because there are many such operators, potential theory strengthens and simplifies the operator theory. Conversely, the set of operators associated with the constraint can influence the potential theory.

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

Nabile Boussaïd,Andrew Comech
Nonlinear Dirac Equation Spectral Stability of Solitary Waves Book PDF

Author : Nabile Boussaïd,Andrew Comech
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 51,8 Mb
Release : 2019-11-21
Category : Education
ISBN : 9781470443955

Get Book

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves by Nabile Boussaïd,Andrew Comech Pdf

This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.

Perverse Sheaves and Applications to Representation Theory

Pramod N. Achar
Perverse Sheaves and Applications to Representation Theory Book PDF

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 49,7 Mb
Release : 2021-09-27
Category : Education
ISBN : 9781470455972

Get Book

Perverse Sheaves and Applications to Representation Theory by Pramod N. Achar Pdf

Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.

Hopf Algebras and Galois Module Theory

Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood
Hopf Algebras and Galois Module Theory Book PDF

Author : Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 41,6 Mb
Release : 2021-11-10
Category : Education
ISBN : 9781470465162

Get Book

Hopf Algebras and Galois Module Theory by Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood Pdf

Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.

Maximal Cohen–Macaulay Modules and Tate Cohomology

Ragnar-Olaf Buchweitz
Maximal Cohen Macaulay Modules and Tate Cohomology Book PDF

Author : Ragnar-Olaf Buchweitz
Publisher : American Mathematical Society
Page : 175 pages
File Size : 50,5 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781470453404

Get Book

Maximal Cohen–Macaulay Modules and Tate Cohomology by Ragnar-Olaf Buchweitz Pdf

This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.

Diagrammatic Algebra

J. Scott Carter,Seiichi Kamada
Diagrammatic Algebra Book PDF

Author : J. Scott Carter,Seiichi Kamada
Publisher : American Mathematical Society
Page : 365 pages
File Size : 49,7 Mb
Release : 2021-12-15
Category : Mathematics
ISBN : 9781470466718

Get Book

Diagrammatic Algebra by J. Scott Carter,Seiichi Kamada Pdf

This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.

Ridge Functions and Applications in Neural Networks

Vugar E. Ismailov
Ridge Functions and Applications in Neural Networks Book PDF

Author : Vugar E. Ismailov
Publisher : American Mathematical Society
Page : 186 pages
File Size : 40,6 Mb
Release : 2021-12-17
Category : Mathematics
ISBN : 9781470467654

Get Book

Ridge Functions and Applications in Neural Networks by Vugar E. Ismailov Pdf

Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.