The mathematics in this volume of the Encyclopaedia, the third in the subseries on PDEs, is more advanced than that in EMS 30 (PDE I). The reader should already be familiar with what is found in that volume. EMS 32 covers in detail two very important topics in PDE: the Cauchy problem and the qualitative theory of second order linear equations. It should be of interest to advanced students and researchers in mathematics and to scientists in neighboring fields with strong mathematical backgrounds.

Klappentext

Two general questions regarding partial differentialequations are explored in detail in this volume of theEncyclopaedia. The first is the Cauchy problem, and itsattendant question of well-posedness (or correctness). Theauthors address this question in the context of PDEs withconstant coefficients and more general convolutionequations in the first two chapters. The third chapterextends a number of these results to equations with variablecoefficients.The second topic is the qualitative theory of second orderlinear PDEs, in particular, elliptic and parabolicequations. Thus, the second part of the book is primarily alook at the behavior of solutions of these equations.There are versions of the maximum principle, thePhragmen-Lindel|f theorem and Harnack's inequality discussedfor both elliptic and parabolic equations.The book is intended for readers who are already familiarwith the basic material in the theory of partialdifferential equations.

Inhalt
I. The Cauchy Problem.- II. Qualitative Theory of Second Order Linear Partial Differential Equations.- Author Index.