附註:Includes bibliographical references (pages 426-430) and index.
Series Preface; Preface; Contents; 1 Introduction; 2 Characteristics; 3 Conservation Laws and Shocks; 4 Maximum Principles; 5 Distributions; 6 Function Spaces; 7 Sobolev Spaces; 8 Operator Theory; 9 Linear Elliptic Equations; 10 Nonlinear Elliptic Equations; 11 Energy Methods for Evolution Problems; 12 Semigroup Methods; A: References; Index.
摘要:"Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Like algebra, topology, and rational mechanics, PDEs are a core area of mathematics." "This book aims to provide the background necessary to initiate work on a Ph. D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in Chapter 10, and the necessary tools from functional analysis are developed within the course. The book can be used to teach a variety of different courses."--Jacket
