Second Order Parabolic Differential Equations

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World Scientific, 1996 - 439 páginas
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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Índice

INTRODUCTION
1
MAXIMUM PRINCIPLES
7
INTRODUCTION TO THE THEORY OF WEAK
21
HOLDER ESTIMATES
45
EXISTENCE UNIQUENESS AND REGULARITY
87
FURTHER THEORY OF WEAK SOLUTIONS
101
STRONG SOLUTIONS
155
FIXED POINT THEOREMS AND THEIR APPLICATIONS
203
BOUNDARY GRADIENT ESTIMATES
231
GLOBAL AND LOCAL GRADIENT BOUNDS
259
HOLDER GRADIENT ESTIMATES AND EXISTENCE
301
THE OBLIQUE DERIVATIVE PROBLEM
321
FULLY NONLINEAR EQUATIONS I INTRODUCTION
361
FULLY NONLINEAR EQUATIONS II HESSIAN
385
Bibliography
421
Index
445

COMPARISON AND MAXIMUM PRINCIPLES
219

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