Second Order Parabolic Differential Equations

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World Scientific, 6 nov 1996 - 452 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

CHAPTER I INTRODUCTION
1
CHAPTER II MAXIMUM PRINCIPLES
7
CHAPTER III INTRODUCTION TO THE THEORY OF WEAK SOLUTIONS
21
CHAPTER IV HÖLDER ESTIMATES
45
CHAPTER V EXISTENCE UNIQUENESS AND REGULARITYOF SOLUTIONS
87
CHAPTER VI FURTHER THEORY OF WEAK SOLUTIONS
101
CHAPTER VII STRONG SOLUTIONS
155
CHAPTER VIII FIXED POINT THEOREMS AND THEIR APPLICATIONS
203
CHAPTER X BOUNDARY GRADIENT ESTIMATES
231
CHAPTER XI GLOBAL AND LOCAL GRADIENT BOUNDS
259
CHAPTER X HÖLDER GRADIENT ESTIMATES AND EXISTENCE THEOREMS
301
CHAPTER XIII THE OBLIQUE DERIVATIVE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS
321
CHAPTER XIV FULLY NONLINEAR EQUATIONS IINTRODUCTION
361
CHAPTER XV FULLY NONLINEAR EQUATIONS II HESSIAN EQUATIONS
385
Bibliography
421
Index
445

CHAPTER IX COMPARISON AND MAXIMUM PRINCIPLES
219

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