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 Content: Front Matter....Pages 1-7 Preface....Pages 9-9 Direct and Inverse Problems in Potential Theory....Pages 11-44 Regularity Results for Some Differential Eouations Associated with Maximal Monotone Operators in Hilbert Spaces....Pages 45-59 Classes D’Interpolation Associées � un Opérateur Monotone ET Applications....Pages 61-72 On Inverse Problems For k-Dimensional Potentials....Pages 73-88 Application of Rothe’s Method to Nonlinear Parabolic Boundary Value Problems....Pages 89-93 Potentials and Removability of Singularities....Pages 95-106 Theorem of Frèchet and Asymptotically Almost Periodic Solutions of Some Nonlinear Equations of Hyperbolic Type....Pages 107-115 A New Type of Generalized Solution of the Dirichlet Problem for the Heat Equation....Pages 117-123 Some Remarks on Dirichlet Problem....Pages 125-132 Diffusion Processes and their Connection to Partial Differential Equations of Parabolic Type....Pages 133-142 Back Matter....Pages 143-145 Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of
