Second Order Parabolic Differential Equations

By: Gary M Lieberman

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Hardcover | 6 November 1996

At a Glance

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462 Pages

Dimensions(cm)
15.9 x 23.5 x 3.2

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This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems. It studies the existence, uniqueness, and regularity of solutions to a variety of problems with Dirichlet boundary conditions and general linear and nonlinear boundary conditions by means of a priori estimates. The first seven chapters give a description of the linear theory and are suitable for a graduate course on partial differential equations. The last eight chapters cover the nonlinear theory for smooth solutions. They include much of the author's research and are aimed at researchers in the field. A unique feature is the emphasis on time-varying domains.

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Preface
Introduction	p. 1
Maximum Principles	p. 7
Introduction to the Theory of Weak Solutions	p. 21
Holder Estimates	p. 45
Existence, Uniqueness, and Regularity of Solutions	p. 87
Further Theory of Weak Solutions	p. 99
Strong Solutions	p. 155
Fixed Point Theorems and Their Applications	p. 197
Comparison and Maximum Principles	p. 213
Boundary Gradient Estimates	p. 223
Global and Local Gradient Bounds	p. 251
Holder Gradient Estimates and Existence Theorems	p. 293
The Oblique Derivative Problem for Quasilinear Parabolic Equations	p. 315
Fully Nonlinear Equations I. Introduction	p. 357
Fully Nonlinear Equations II. Hessian Equations	p. 383
References	p. 419
Index	p. 437
Table of Contents provided by Blackwell. All Rights Reserved.

Second Order Parabolic Differential Equations

At a Glance

Hardcover

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