Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains

Author : Mikhail S. Agranovich
Publisher : Springer
Page : 331 pages
File Size : 43,8 Mb
Release : 2015-05-06
Category : Mathematics
ISBN : 9783319146485

Get Book

Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains by Mikhail S. Agranovich Pdf

This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.

Author : Malcolm Brown,Fritz Gesztesy,Pavel Kurasov,Ari Laptev,Barry Simon,Gunter Stolz,Ian Wood
Publisher : Springer Nature
Page : 731 pages
File Size : 50,5 Mb
Release : 2023-09-21
Category : Mathematics
ISBN : 9783031311390

Get Book

From Complex Analysis to Operator Theory: A Panorama by Malcolm Brown,Fritz Gesztesy,Pavel Kurasov,Ari Laptev,Barry Simon,Gunter Stolz,Ian Wood Pdf

This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Author : Christian Constanda,Bardo E.J. Bodmann,Paul J. Harris
Publisher : Springer Nature
Page : 407 pages
File Size : 40,8 Mb
Release : 2023-10-31
Category : Mathematics
ISBN : 9783031340994

Get Book

Integral Methods in Science and Engineering by Christian Constanda,Bardo E.J. Bodmann,Paul J. Harris Pdf

This volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Seventeenth International Conference on Integral Methods in Science and Engineering, held virtually in July 2022, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.

Author : Vladimir Maz'ya
Publisher : Springer Science & Business Media
Page : 882 pages
File Size : 41,8 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9783642155642

Get Book

Sobolev Spaces by Vladimir Maz'ya Pdf

Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.

Author : Jussi Behrndt,Seppo Hassi,Henk de Snoo
Publisher : Springer Nature
Page : 772 pages
File Size : 50,9 Mb
Release : 2020-01-03
Category : Mathematics
ISBN : 9783030367145

Get Book

Boundary Value Problems, Weyl Functions, and Differential Operators by Jussi Behrndt,Seppo Hassi,Henk de Snoo Pdf

This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

Author : Dorothee Haroske,Hans Triebel
Publisher : European Mathematical Society
Page : 312 pages
File Size : 49,8 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190426

Get Book

Distributions, Sobolev Spaces, Elliptic Equations by Dorothee Haroske,Hans Triebel Pdf

It is the main aim of this book to develop at an accessible, moderate level an $L_2$ theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev spaces on domains and on their boundaries, together with a related spectral theory. The presentation is preceded by an introduction to the classical theory for the Laplace-Poisson equation, and some chapters provide required ingredients such as the theory of distributions, Sobolev spaces and the spectral theory in Hilbert spaces. The book grew out of two-semester courses the authors have given several times over a period of ten years at the Friedrich Schiller University of Jena. It is addressed to graduate students and mathematicians who have a working knowledge of calculus, measure theory and the basic elements of functional analysis (as usually covered by undergraduate courses) and who are seeking an accessible introduction to some aspects of the theory of function spaces and its applications to elliptic equations.

Author : Francisco J. Sayas,Thomas S. Brown,Matthew E. Hassell
Publisher : CRC Press
Page : 492 pages
File Size : 41,5 Mb
Release : 2019-01-16
Category : Mathematics
ISBN : 9780429016202

Get Book

Variational Techniques for Elliptic Partial Differential Equations by Francisco J. Sayas,Thomas S. Brown,Matthew E. Hassell Pdf

Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics

Author : Sergei Rogosin,Ahmet Okay Çelebi
Publisher : Springer
Page : 318 pages
File Size : 42,7 Mb
Release : 2019-01-30
Category : Mathematics
ISBN : 9783030026509

Get Book

Analysis as a Life by Sergei Rogosin,Ahmet Okay Çelebi Pdf

This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday. It aims at being a tribute to the excellent achievements of Heinrich Begehr in complex analysis and complex differential equations, and especially to his prominent role as one of the creators and long-time leader of the International Society for Analysis, its Applications and Computation (ISAAC).

Author : Ionuţ Munteanu
Publisher : Springer
Page : 214 pages
File Size : 48,8 Mb
Release : 2019-02-15
Category : Science
ISBN : 9783030110994

Get Book

Boundary Stabilization of Parabolic Equations by Ionuţ Munteanu Pdf

This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling. The text provides answers to the following problems, which are of great practical importance: Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state Designing observers for the considered control systems Constructing time-discrete controllers requiring only partial knowledge of the state After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more. Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.

Author : Konrad Schmüdgen
Publisher : Springer Nature
Page : 381 pages
File Size : 52,7 Mb
Release : 2020-07-28
Category : Mathematics
ISBN : 9783030463663

Get Book

An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space by Konrad Schmüdgen Pdf

This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

Author : Andrei Ludu
Publisher : MDPI
Page : 122 pages
File Size : 41,7 Mb
Release : 2020-04-16
Category : Mathematics
ISBN : 9783039287260

Get Book

The Application of Mathematics to Physics and Nonlinear Science by Andrei Ludu Pdf

Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natural patterns, and coupled interactions between components or different scales are only a few examples of systems where nonlinear science is necessary. All outstanding, self-sustained, and stable structures in space and time exist and protrude out of a regular linear background of states mainly because they identify themselves from the rest by being highly localized in range, time, configuration, states, and phase spaces. Guessing how high up you drive toward the top of the mountain by compiling your speed, road slope, and trip duration is a linear model, but predicting the occurrence around a turn of a boulder fallen on the road is a nonlinear phenomenon. In an effort to grasp and understand nonlinear phenomena, scientists have developed several mathematical approaches including inverse scattering theory, Backlund and groups of transformations, bilinear method, and several other detailed technical procedures. In this Special Issue, we introduce a few very recent approaches together with their physical meaning and applications. We present here five important papers on waves, unsteady flows, phases separation, ocean dynamics, nonlinear optic, viral dynamics, and the self-appearance of patterns for spatially extended systems, which are problems that have aroused scientists’ interest for decades, yet still cannot be predicted and have their generating mechanism and stability open to debate. The aim of this Special Issue was to present these most debated and interesting topics from nonlinear science for which, despite the existence of highly developed mathematical tools of investigation, there are still fundamental open questions.

Author : Dmitry Balandin,Konstantin Barkalov,Victor Gergel,Iosif Meyerov
Publisher : Springer Nature
Page : 418 pages
File Size : 40,5 Mb
Release : 2021-06-23
Category : Computers
ISBN : 9783030787592

Get Book

Mathematical Modeling and Supercomputer Technologies by Dmitry Balandin,Konstantin Barkalov,Victor Gergel,Iosif Meyerov Pdf

This book constitutes selected and revised papers from the 20th International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2020, held in Nizhny Novgorod, Russia, in November 2020. Due to the COVID-19 pandemic the conference was held online. The 25 full papers and 8 short papers presented in the volume were thoroughly reviewed and selected from the 106 submissions. They are organized in topical secions on ​computational methods for mathematical models analysis; computation in optimization and optimal control; supercomputer simulation.

Author : DOROTHEE D. HAROSKE; HANS TRIEBEL.
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 3037195428

Get Book

DISTRIBUTIONS, SOBOLEV SPACES, ELLIPTIC EQUATIONS. by DOROTHEE D. HAROSKE; HANS TRIEBEL. Pdf

Author : Eugene G. D'yakonov
Publisher : CRC Press
Page : 379 pages
File Size : 44,6 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351092111

Get Book

Optimization in Solving Elliptic Problems by Eugene G. D'yakonov Pdf

Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics - the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a pre-determined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multi-dimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and Navier-Stokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokes-type problems, methods of solving fourth-order problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems. The mathematics necessary to understand the development of such algorithms is provided in the introductory material within the text, and common specifications of algorithms that have been developed for typical problems in mathema

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 45,7 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

Get Book

Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.