Potential Theory

Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in­ cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal with applications in physics and engineering, other concern potential­ theoretic aspects of function theory and complex analysis. Numerous papers are devoted to the theory of partial differential equations. Included are also many articles on axiomatic and abstract potential theory with its relations to probability theory. The present volume may thus be of intrest to mathematicians speciali­ zing in the above-mentioned fields and also to everybody interested in the present state of potential theory as a whole.

On Weighted Beppo Levi Functions.- Generalized Cauchy-Riemann Equations and the Positive k-Subharmonie Functions.- Iteration Methods for Potential Problems.- On the Poisson Equation on the Infinite Dimensional Torus.- A Characterization of Elementary Potential Theory.- Wiener Estimates for Solutions of Elliptic Equations in Nondivergence Form.- Approximation by Continuous Potentials.- The Schrö;dinger Equation ? u = ? u in a Neighbourhood of an Isolated Singularity of ?.- A Characterization of the Fine Sheaf Property.- Harmonic Morphisms and Ray Processes.- On Dirichlet’s Boundary Value Problem for Certain Anisotropic Differential and Pseudo-Differential Operators.- Hyperharmonic Cones.- Jump Relations for Surface Potentials in Case of Continuous Densities.- On a Unified Characterization of Capacity.- A Note on the Computation of Green Functions for Sublaplacians on Lie Algebras of Type H.- On Thermoelastic Potential.- The Dirichlet Problem on Ends.- Diffusion Kernels of Logarithmic Type.- A Remark on Capacitary Measures for Diffusion Processes.- On the Convexity of Level Sets for Elliptic and Parabolic Exterior Boundary Value Problems.- Harnack Inequality and Some Characteristics of Non-Regular Points of Simplexes.- Polar Sets in a Nonlinear Potential Theory.- A Sharper Form of a Theorem of Kolmagorov.- Extremal Problems for the Distributed Moment Problem.- On Mathematical Modelling of Non-Newtonian Flow by Perturbation Methods.- On Diffusion Semigroups Generated by Semi-Elliptic Differential Operators in Infinite Dimensions.- The Obstacle Problem in a Non-Linear Potential Theory.- On the Appell Transformation.- Perturbation and Excessive Functions.- Capacities on Harmonic Spaces with Adjoint Structure.- Balayage Spaces on Topological Sums.- Subordination forBalayage Spaces.- On the New Problem in the Potential Gravity Theory.- Stochastic Differentiation Formula and Convergence Theorem for Finely Hyperharmonic Functions.- Morphisms of Stonian Cones.- On the Transition Function of the Infinite Dimensional Ornstein-Uhlenbeck Process Given by the Free Quantum Field.- Finiteness of the Family of Simply Connected Quadrature Domains.- On an Inverse Problem for the Newtonian Potential.- On the Integration of Elastostatic Displacement Equation.- Non-Linear Potential Theory in Lebesgue Spaces with Mixed Norm.- Schroedinger Equations with Discontinuous Solutions.- Polynomial Hulls and Envelopes of Holomorphy.- Green Function and Uniform Harnack Inequality.- On the Asymptotic Behavior of Solutions of a System of Integral Equations of Mixed Boundary Value Problem of Plane Elasticity in a Neighborhood of Corner Points of the Contour.