Second Order Parabolic Differential EquationsWorld 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. |
Índice
INTRODUCTION | 1 |
MAXIMUM PRINCIPLES | 7 |
INTRODUCTION TO THE THEORY OF WEAK | 21 |
HÖLDER ESTIMATES | 45 |
EXISTENCE UNIQUENESS AND REGULARITY | 87 |
FURTHER THEORY OF WEAK SOLUTIONS | 101 |
Notes | 150 |
FIXED POINT THEOREMS AND THEIR APPLICATIONS | 203 |
BOUNDARY GRADIENT ESTIMATES | 231 |
GLOBAL AND LOCAL GRADIENT BOUNDS | 259 |
HÖLDER GRADIENT ESTIMATES AND EXISTENCE | 301 |
THE OBLIQUE DERIVATIVE PROBLEM | 321 |
FULLY NONLINEAR EQUATIONS I INTRODUCTION | 361 |
FULLY NONLINEAR EQUATIONS II HESSIAN | 385 |
| 421 | |
| 445 | |
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Términos y frases comunes
a₁ a¹º argument assume b₁ boundary condition boundary gradient estimate c₁ Cauchy-Dirichlet problem Chapter coefficients constant C determined Corollary cylinder D²u define differential equation domain elliptic equations existence result existence theorem follows fully nonlinear gives global gradient bound H1+a H2+a Harnack inequality hence Hölder continuous Hölder estimate Hölder gradient estimate Hölder's inequality holds hypotheses implies infer integral Lemma linear Lipschitz M₁ matrix maximum principle mean curvature modulus of continuity Monge-Ampère equation nonnegative constant norm oblique derivative problem parabolic equations positive constants proof of Theorem Proposition prove quasilinear Rn+1 satisfies Section shows solvability subset subsolution sup|u Suppose supu u₁ uniformly parabolic v₁ value problem vector w₁ weak derivatives weak solution X₁ ΒΩ λο ΡΩ
Referencias a este libro
Diffusions, Superdiffusions, and Partial Differential ..., Volumen 5;Volumen 50 Evgeniĭ Borisovich Dynkin No hay ninguna vista previa disponible - 2002 |