Regularity Results For Nonlocal Fully Nonlinear Elliptic Equations
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Regularity Results For Nonlocal Fully Nonlinear Elliptic Equations
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Author : Marcus Rang
language : en
Publisher:
Release Date : 2013
Regularity Results For Nonlocal Fully Nonlinear Elliptic Equations written by Marcus Rang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Fully Nonlinear Elliptic Equations
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Author : Luis A. Caffarelli
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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.
Integro Differential Elliptic Equations
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Author : Xavier Fernández-Real
language : en
Publisher: Springer Nature
Release Date : 2024-04-24
Integro Differential Elliptic Equations written by Xavier Fernández-Real and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.
This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters.
Regularity Techniques For Elliptic Pdes And The Fractional Laplacian
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Author : Pablo Raúl Stinga
language : en
Publisher: CRC Press
Release Date : 2024-06-21
Regularity Techniques For Elliptic Pdes And The Fractional Laplacian written by Pablo Raúl Stinga and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-21 with Mathematics categories.
Regularity Techniques for Elliptic PDEs and the Fractional Laplacian presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian. The emphasis is placed on ideas and the development of intuition, while at the same time being completely rigorous. The reader should keep in mind that this text is about how analysis can be applied to regularity estimates. Many methods are nonlinear in nature, but the focus is on linear equations without lower order terms, thus avoiding bulky computations. The philosophy underpinning the book is that ideas must be flushed out in the cleanest and simplest ways, showing all the details and always maintaining rigor. Features Self-contained treatment of the topic Bridges the gap between upper undergraduate textbooks and advanced monographs to offer a useful, accessible reference for students and researchers. Replete with useful references.
Variational Methods For Nonlocal Fractional Problems
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Author : Giovanni Molica Bisci
language : en
Publisher: Cambridge University Press
Release Date : 2016-03-11
Variational Methods For Nonlocal Fractional Problems written by Giovanni Molica Bisci and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-11 with Mathematics categories.
This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.
Elliptic Partial Differential Equations
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Author : Lucio Boccardo
language : en
Publisher: Walter de Gruyter
Release Date : 2013-10-29
Elliptic Partial Differential Equations written by Lucio Boccardo and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-29 with Mathematics categories.
Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
The Obstacle Problem
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Author : Luis Angel Caffarelli
language : en
Publisher: Edizioni della Normale
Release Date : 1999-10-01
The Obstacle Problem written by Luis Angel Caffarelli and has been published by Edizioni della Normale this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-01 with Mathematics categories.
The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.
Analysis And Partial Differential Equations On Manifolds Fractals And Graphs
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Author : Alexander Grigor'yan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-01-18
Analysis And Partial Differential Equations On Manifolds Fractals And Graphs written by Alexander Grigor'yan and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Mathematics categories.
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Several Regularity Results For Nonlocal Elliptic Equations
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Author : Hui Yu (Ph. D.)
language : en
Publisher:
Release Date : 2017
Several Regularity Results For Nonlocal Elliptic Equations written by Hui Yu (Ph. D.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Nonlocal elliptic equations have long been used by physicists and engineers to model diffusion processes involving jumps. Apart from several works from a probabilistic view, there had not been much development concerning their mathematical properties until the fundamental works of Caffarelli and Silvestre. Here we establish several results concerning the regularity of viscosity solutions to nonlocal elliptic equations. In particular, we show the existence of smooth solutions to two class of nonlocal fully nonlinear elliptic equations, an integrability estimate for the fractional order Hessian of solutions to nonlocal equations, as well as a theory of at solutions.
Nonlinear Partial Differential Equations And Related Topics
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Author : Arina A. Arkhipova
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Nonlinear Partial Differential Equations And Related Topics written by Arina A. Arkhipova and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"St. Petersburg PDE seminar, special session dedicated to N.N. Uraltseva's [75th] anniversary, June 2009"--P. [vi].