Integro Differential Elliptic Equations

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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.

Applied Stochastic Control Of Jump Diffusions

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Author : Bernt Øksendal
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-26

Applied Stochastic Control Of Jump Diffusions written by Bernt Øksendal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-26 with Mathematics categories.

Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

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.

Finite Element Methods For Integrodifferential Equations

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Author : Chuan Miao Chen
language : en
Publisher: World Scientific
Release Date : 1998-02-28

Finite Element Methods For Integrodifferential Equations written by Chuan Miao Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-28 with Mathematics categories.

Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas. Such equations possess new physical and mathematical properties. This monograph systematically discusses application of the finite element methods to numerical solution of integrodifferential equations. It will be useful for numerical analysts, mathematicians, physicists and engineers. Advanced undergraduates and graduate students should also find it beneficial.

Inverse Problems For Integro Differential Operators

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Author : Yi-Hsuan Lin
language : en
Publisher: Springer Nature
Release Date :

Inverse Problems For Integro Differential Operators written by Yi-Hsuan Lin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Integro Differential Operators

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Author : Reshma Menon
language : en
Publisher:
Release Date : 2020

Integro Differential Operators written by Reshma Menon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Electronic dissertations categories.

In this dissertation, we study aspects of integro-differential operators, and how they relate to different types of equations. In each case, we use information and results about the operators in a lower dimension to analyse an equation in a higher dimension, and vice-versa. We begin in chapter 1 with an introduction to the operators and equations we will be considering.In Chapters 2 and 3, we discuss certain integro-differential operators of functions in a relatively smooth space. However, to understand more about the structure of these operators, particularly about the measure associated with them, we study certain equations in a higher dimension such as degenerate elliptic equations in the upper half space. We analyse the solution of such an equation and its gradient, followed by estimates on its Green's function and Poisson kernel. These estimates then help reveal some properties of the measure associated with the integro-differential operator in the lower dimension. The structure of the degenerate elliptic equations is similar to that of uniformly elliptic equations, but with an additional complexity of a term which involves distance to the boundary. This degeneracy complicates the analysis; as such, the classical techniques of finding pointwise estimates as mentioned above do not work so well anymore. So we provide some revised results for the same. Thus understanding an equation in a higher dimension gives us information about an integro-differential operator in a lower dimension.In Chapters 4 and 5, we prove some results about the solutions of free boundary problems in Rn+1 x [0, T], where the free boundary for a fixed time t can be seen as the graph of a function over a sphere. This time, we connect the solution of the free boundary problem to the solution of a parabolic equation on the sphere - that is, in a lower dimension. This parabolic equation involves an integro-differential operator, which has a min-max representation that is consistent with all the results about viscosity solutions of parabolic equations in Rn. We modify these results for parabolic equations on the sphere, which then gives us existence and uniqueness results about the free boundary problem in a higher dimension.

Selected Papers Of Antoni Zygmund

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Author : A. Hulanicki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Selected Papers Of Antoni Zygmund written by A. Hulanicki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Partial Integral Operators And Integro Differential Equations

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Author : Jurgen Appell
language : en
Publisher: CRC Press
Release Date : 2000-02-29

Partial Integral Operators And Integro Differential Equations written by Jurgen Appell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-29 with Mathematics categories.

A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linea

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.

Ill Posed Problems For Integrodifferential Equations In Mechanics And Electromagnetic Theory

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Author : Frederick Bloom
language : en
Publisher: SIAM
Release Date : 1981-10-01

Ill Posed Problems For Integrodifferential Equations In Mechanics And Electromagnetic Theory written by Frederick Bloom and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-10-01 with Science categories.

Examines initial-history boundary-value problems associated with systems of partial-integrodifferential equations arising in mechanics and electromagnetic theories.