The New Method Of Regularity Theory And Its Applications

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The New Method of Regularity Theory and Its Applications

Shuhong Chen,Zhong Tan
The New Method of Regularity Theory and Its Applications Book PDF

Author : Shuhong Chen,Zhong Tan
Publisher : LAP Lambert Academic Publishing
Page : 296 pages
File Size : 41,5 Mb
Release : 2012
Category : Analytic functions
ISBN : 3659278068

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The New Method of Regularity Theory and Its Applications by Shuhong Chen,Zhong Tan Pdf

Regularity theory is one of the most challenging problems in modern theory of partial differential equations. It has attracted peoples' eyes for a long history. A classical method of partial regularity theory is the "freezing the coefficients" method. The proof is complex and troublesome. And the result obtained by this method is not optimal. In this book, we use the method of A-harmonic approximation, to consider regularity theory for nonlinear partial differential systems. The new method not only allows one to simplify the procedure of proof, but also to establish optimal regularity results directly. This book should be useful to professionals in partial differential equations.

Regularity Results for Nonlinear Elliptic Systems and Applications

Alain Bensoussan,Jens Frehse
Regularity Results for Nonlinear Elliptic Systems and Applications Book PDF

Author : Alain Bensoussan,Jens Frehse
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 49,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662129050

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Regularity Results for Nonlinear Elliptic Systems and Applications by Alain Bensoussan,Jens Frehse Pdf

This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.

Regularity Theory for Mean Curvature Flow

Klaus Ecker
Regularity Theory for Mean Curvature Flow Book PDF

Author : Klaus Ecker
Publisher : Springer Science & Business Media
Page : 165 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817682101

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Regularity Theory for Mean Curvature Flow by Klaus Ecker Pdf

* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.

Regularity Concepts in Nonsmooth Analysis

Messaoud Bounkhel
Regularity Concepts in Nonsmooth Analysis Book PDF

Author : Messaoud Bounkhel
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 48,8 Mb
Release : 2011-11-12
Category : Mathematics
ISBN : 9781461410195

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Regularity Concepts in Nonsmooth Analysis by Messaoud Bounkhel Pdf

The results presented in this book are a product of research conducted by the author independently and in collaboration with other researchers in the field. In this light, this work encompasses the most recent collection of various concepts of regularity and nonsmooth analysis into one monograph. The first part of the book attempts to present an accessible and thorough introduction to nonsmooth analysis theory. Main concepts and some useful results are stated and illustrated through examples and exercises. The second part gathers the most prominent and recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis. The third and final section contains six different application, with comments in relation to the existing literature.

Regularity Theory for Mean Curvature Flow

Klaus Ecker
Regularity Theory for Mean Curvature Flow Book PDF

Author : Klaus Ecker
Publisher : Unknown
Page : 165 pages
File Size : 42,6 Mb
Release : 2004
Category : Courbure
ISBN : 3764332433

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Regularity Theory for Mean Curvature Flow by Klaus Ecker Pdf

This work is devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics. A major example is Hamilton's Ricci flow program, which has the aim of settling Thurston's geometrization conjecture, with recent major progress due to Perelman. Another important application of a curvature flow process is the resolution of the famous Penrose conjecture in general relativity by Huisken and Ilmanen. Under mean curvature flow, surfaces usually develop singularities in finite time. This work presents techniques for the study of singularities of mean curvature flow and is largely based on the work of K. Brakke, although more recent developments are incorporated.

Agricultural Survey Methods

Roberto Benedetti,Federica Piersimoni,Marco Bee,Giuseppe Espa
Agricultural Survey Methods Book PDF

Author : Roberto Benedetti,Federica Piersimoni,Marco Bee,Giuseppe Espa
Publisher : John Wiley & Sons
Page : 434 pages
File Size : 53,8 Mb
Release : 2010-03-18
Category : Mathematics
ISBN : 0470665467

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Agricultural Survey Methods by Roberto Benedetti,Federica Piersimoni,Marco Bee,Giuseppe Espa Pdf

Due to the widespread use of surveys in agricultural resources estimation there is a broad and recognizable interest in methods and techniques to collect and process agricultural data. This book brings together the knowledge of academics and experts to increase the dissemination of the latest developments in agricultural statistics. Conducting a census, setting up frames and registers and using administrative data for statistical purposes are covered and issues arising from sample design and estimation, use of remote sensing, management of data quality and dissemination and analysis of survey data are explored. Key features: Brings together high quality research on agricultural statistics from experts in this field. Provides a thorough and much needed overview of developments within agricultural statistics. Contains summaries for each chapter, providing a valuable reference framework for those new to the field. Based upon a selection of key methodological papers presented at the ICAS conference series, updated and expanded to address current issues. Covers traditional statistical methodologies including sampling and weighting. This book provides a much needed guide to conducting surveys of land use and to the latest developments in agricultural statistics. Statisticians interested in agricultural statistics, agricultural statisticians in national statistics offices and statisticians and researchers using survey methodology will benefit from this book.

Quantitative Stochastic Homogenization and Large-Scale Regularity

Scott Armstrong,Tuomo Kuusi,Jean-Christophe Mourrat
Quantitative Stochastic Homogenization and Large Scale Regularity Book PDF

Author : Scott Armstrong,Tuomo Kuusi,Jean-Christophe Mourrat
Publisher : Springer
Page : 518 pages
File Size : 46,7 Mb
Release : 2019-05-09
Category : Mathematics
ISBN : 9783030155452

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Quantitative Stochastic Homogenization and Large-Scale Regularity by Scott Armstrong,Tuomo Kuusi,Jean-Christophe Mourrat Pdf

The focus of this book is the large-scale statistical behavior of solutions of divergence-form elliptic equations with random coefficients, which is closely related to the long-time asymptotics of reversible diffusions in random media and other basic models of statistical physics. Of particular interest is the quantification of the rate at which solutions converge to those of the limiting, homogenized equation in the regime of large scale separation, and the description of their fluctuations around this limit. This self-contained presentation gives a complete account of the essential ideas and fundamental results of this new theory of quantitative stochastic homogenization, including the latest research on the topic, and is supplemented with many new results. The book serves as an introduction to the subject for advanced graduate students and researchers working in partial differential equations, statistical physics, probability and related fields, as well as a comprehensive reference for experts in homogenization. Being the first text concerned primarily with stochastic (as opposed to periodic) homogenization and which focuses on quantitative results, its perspective and approach are entirely different from other books in the literature.

Nonlinear Functional Analysis and its Applications

E. Zeidler
Nonlinear Functional Analysis and its Applications Book PDF

Author : E. Zeidler
Publisher : Springer Science & Business Media
Page : 675 pages
File Size : 46,5 Mb
Release : 2013-12-11
Category : Science
ISBN : 9781461250203

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Nonlinear Functional Analysis and its Applications by E. Zeidler Pdf

As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? ( y) What typical applications are there? Vll Preface viii Special emphasis is placed on motivation.

Probabilistic Theory of Mean Field Games with Applications I

René Carmona,François Delarue
Probabilistic Theory of Mean Field Games with Applications I Book PDF

Author : René Carmona,François Delarue
Publisher : Springer
Page : 714 pages
File Size : 41,6 Mb
Release : 2018-03-01
Category : Mathematics
ISBN : 9783319589206

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Probabilistic Theory of Mean Field Games with Applications I by René Carmona,François Delarue Pdf

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Elliptic Regularity Theory by Approximation Methods

Edgard A. Pimentel
Elliptic Regularity Theory by Approximation Methods Book PDF

Author : Edgard A. Pimentel
Publisher : Cambridge University Press
Page : 203 pages
File Size : 48,8 Mb
Release : 2022-09-29
Category : Mathematics
ISBN : 9781009096669

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Elliptic Regularity Theory by Approximation Methods by Edgard A. Pimentel Pdf

A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.

Singularity Theory and its Applications

David Mond,James Montaldi
Singularity Theory and its Applications Book PDF

Author : David Mond,James Montaldi
Publisher : Springer
Page : 416 pages
File Size : 44,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540470601

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Singularity Theory and its Applications by David Mond,James Montaldi Pdf

A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory, and applications in the sciences. The papers are orginal research, stimulated by the symposium and workshops: All have been refereed, and none will appear elsewhere. The main topic, deformation theory, is represented by several papers on descriptions of the bases of versal deformations, and several more on descriptions of the generic fibres. Other topics include stratifications, and applications to differential geometry.

Iterative Methods for Approximate Solution of Inverse Problems

A.B. Bakushinsky,M.Yu. Kokurin
Iterative Methods for Approximate Solution of Inverse Problems Book PDF

Author : A.B. Bakushinsky,M.Yu. Kokurin
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 42,9 Mb
Release : 2007-09-28
Category : Mathematics
ISBN : 9781402031229

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Iterative Methods for Approximate Solution of Inverse Problems by A.B. Bakushinsky,M.Yu. Kokurin Pdf

This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering. The volume can be read by anyone with a basic knowledge of functional analysis. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.

Future Perspectives in Risk Models and Finance

Alain Bensoussan,Dominique Guegan,Charles S. Tapiero
Future Perspectives in Risk Models and Finance Book PDF

Author : Alain Bensoussan,Dominique Guegan,Charles S. Tapiero
Publisher : Springer
Page : 315 pages
File Size : 44,9 Mb
Release : 2014-11-20
Category : Business & Economics
ISBN : 9783319075242

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Future Perspectives in Risk Models and Finance by Alain Bensoussan,Dominique Guegan,Charles S. Tapiero Pdf

This book provides a perspective on a number of approaches to financial modelling and risk management. It examines both theoretical and practical issues. Theoretically, financial risks models are models of a real and a financial “uncertainty”, based on both common and private information and economic theories defining the rules that financial markets comply to. Financial models are thus challenged by their definitions and by a changing financial system fueled by globalization, technology growth, complexity, regulation and the many factors that contribute to rendering financial processes to be continuously questioned and re-assessed. The underlying mathematical foundations of financial risks models provide future guidelines for risk modeling. The book’s chapters provide selective insights and developments that can contribute to better understand the complexity of financial modelling and its ability to bridge financial theories and their practice. Future Perspectives in Risk Models and Finance begins with an extensive outline by Alain Bensoussan et al. of GLM estimation techniques combined with proofs of fundamental results. Applications to static and dynamic models provide a unified approach to the estimation of nonlinear risk models. A second section is concerned with the definition of risks and their management. In particular, Guegan and Hassani review a number of risk models definition emphasizing the importance of bi-modal distributions for financial regulation. An additional chapter provides a review of stress testing and their implications. Nassim Taleb and Sandis provide an anti-fragility approach based on “skin in the game”. To conclude, Raphael Douady discusses the noncyclical CAR (Capital Adequacy Rule) and their effects of aversion of systemic risks. A third section emphasizes analytic financial modelling approaches and techniques. Tapiero and Vallois provide an overview of mathematical systems and their use in financial modeling. These systems span the fundamental Arrow-Debreu framework underlying financial models of complete markets and subsequently, mathematical systems departing from this framework but yet generalizing their approach to dynamic financial models. Explicitly, models based on fractional calculus, on persistence (short memory) and on entropy-based non-extensiveness. Applications of these models are used to define a modeling approach to incomplete financial models and their potential use as a “measure of incompleteness”. Subsequently Bianchi and Pianese provide an extensive overview of multi-fractional models and their important applications to Asset price modeling. Finally, Tapiero and Jinquyi consider the binomial pricing model by discussing the effects of memory on the pricing of asset prices.

Mathematical and Computational Techniques for Multilevel Adaptive Methods

Ulrich Ruede
Mathematical and Computational Techniques for Multilevel Adaptive Methods Book PDF

Author : Ulrich Ruede
Publisher : SIAM
Page : 152 pages
File Size : 50,9 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 9780898713206

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Mathematical and Computational Techniques for Multilevel Adaptive Methods by Ulrich Ruede Pdf

This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures.

Nonsmooth Equations in Optimization

Diethard Klatte,B. Kummer
Nonsmooth Equations in Optimization Book PDF

Author : Diethard Klatte,B. Kummer
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 54,8 Mb
Release : 2005-12-17
Category : Mathematics
ISBN : 9780306476167

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Nonsmooth Equations in Optimization by Diethard Klatte,B. Kummer Pdf

Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.