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Fully nonlinear elliptic equations

Author: Luis A Caffarelli; Xavier Cabré
Publisher: Providence, R.I. : American Mathematical Society, ©1995.
Series: Colloquium publications (American Mathematical Society), v. 43.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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,  Read more...
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Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Luis A Caffarelli; Xavier Cabré
ISBN: 9781470431891 1470431890
OCLC Number: 956663966
Description: 1 online resource.
Contents: Introduction Chapter 1. Preliminaries Chapter 2. Viscosity solutions of elliptic equations Chapter 3. Alexandroff estimate and maximum principle Chapter 4. Harnack inequality Chapter 5. Uniqueness of solutions Chapter 6. Concave equations Chapter 7. $W^{2,p}$ Regularity Chapter 8. Hölder regularity Chapter 9. The Dirichlet problem for concave equations.
Series Title: Colloquium publications (American Mathematical Society), v. 43.
Responsibility: Luis A. Caffarelli, Xavier Cabré.

Abstract:

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 equa.

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