Nonlinear Evolution Equations and Potential Theory

During . recent years, the Mathematical Institute of the Czechoslovak Academy of Sciences has organized summer schools de- voted to non~linear functional analysis and its applications- particularly in the theory of boundary value problems for dif- ferential equations. The main subj ects of the summer school held from 24 to 29 Sep- tember 1973 at Podhradi near Ledec on Sazava were theory of non- linear evolution equations and potential theory. The summer school was attended by more than 60 mathematicians from Czechoslovakia and abroad. The lectures were delivered by Gottfried Anger, Halle (GDR), Viorel Barbu, Ia~i (Romania), Haim Brezis, Paris (France), Siegfried nUmmel, Karl-Marx-Stadt (GDR), Jozef Kacur, Bratislava (Czechoslovakia), Josef Kral, Praha (Czechoslovakia), S. N. Kruzkov, Moskva (USSR), Vladimir Lovicar, Praha (Czechoslovakia), Jaroslav Lukes, Praha (Czechoslovakia), Jifi Vesely, Praha (Czechoslovakia), Ivo Vrkoc, Praha (Czechoslovakia). In the present proceedings the text of almost all lectures delivered during the school are collected. Josef Krel Editor September, 1974 DIRECT AND INVERSE PROBLEMS IN POTENTIAL THEORY Gottfried Anger Halle (GDR) The aim of this paper is to sketch the most important direct problems (boundary value problems and initial value problems) of linear elliptic, paraboli"c and hyperbolic differential equations and some inverse problems corresponding to these equations. Both types of problems are divided into two classes. The first one is the class of properly posed problems, the other is the class of improperly posed problems.