内容简介
This book deals with nonlinear parabolic equations and systems of second order in higher dimensional domains, mainly several initial-boundary value problems for nonlinear parabolic equations and systems of second order equations with smooth coefficients or measuxrable coefficients are discussed. There are two characteristics of this book. One is that parabolic equations are discussed in the nonlinear case and the boundary conditions include the irregular oblique derivative case, another one is that boundary value problems are almost considered in the case of multiply connected domains and several methods are used. This book can be refered to the graduate students, reseachers in partial differential equations and function theory at universities and institutes.
目录
Preface Chapter I Properties of Solutions for Parabolic Equations of Second Order 1. Conditions of Linear and Nonlinear Parabolic Equations of Second Order 2. Extremum Principles of Solutions for Parabolic Equations of Second Order 3. Uniqueness and Stability of Solutions for Some Initial-Boundary Value Problems 4. Representation Theorem and Compactness Principle of Solutions for Parabolic Equations 5. Aleksandrov-Bakel''man-Pucci Type Maximum Principle Chapter II Nonlinear Parabolic Equations of Second Order with Smooth Coefficients 1. Formulation of Initial-Irregular Oblique Derivative Problem for Nonlinear Parabolic Equations with Smooth Coefficients 2. Boundedness and Hhlder Estimates of Solutions of InitialRegular Oblique Derivative Problem for Equation 1.2 3. Boundedness and Hhlder Estimates of Derivatives of Solutions of Initial-Regular Oblique Derivative Problem for Equation 1.2 4. A Priori Estimates of Derivatives of Solutions of Initial-Irregular Oblique Derivative Problem for Equation 1.2 5. Solvability of the Initial-Irregular Oblique Derivative Problem for Equation 1.2 Chapter III Nonlinear Parabolic Equations of Second Order with Cordes Measurable Coefficients 1. Formulation of Initial-Boundary Value Problems for Nonlinear Parabolic Equations 2. Inner Estimates of Solutions of Initial-Boundary Value Problems for Parabolic Equations 3. The Dirichlet Problem and Nuemann Problem for Nonlinear Parabolic Equations 4. Initial-Oblique Derivative Problem for Nonlinear Parabolic Equations 5. Initial-Mixed Boundary Value Problems for Nonlinear Parabolic Equations Chapter IV Nonlinear Parabolic Systems of Equations with Cordes Measurable Coefficients 1. Formulation of Initial-Oblique Derivative Problems for Nonlinear Parabolic Systems 2. Solvability of Problem D and Problem N for Parabolic Systems of Second Order Equations 3. Initial-Oblique Derivative Boundary Value Problem for Nonlinear Parabolic Systems 4. Initial-Mixed Boundary Value Problem for Nonlinear Parabolic Systems Chapter V Linear and Quasilinear Parabolic Equations with VMO Measurable Coefficients 1. Some Results of Harmonic Analysis and Fundamental Solutions of Parabolic Equations 2. Interior Representation and Dirichlet Boundary Value Problem for Linear Parabolic Equations 3. Initial-Oblique Derivative Boundary Value Problems for Linear Parabolic Equations 4. Quasilinear Parabolic Equations with Regular Boundary Conditions References
