Potential Theory -

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Résumé :
The volume comprises eleven survey papers based on survey lectures delivered at the Conference in Prague in July 1987, which covered various facets of potential theory, including its applications in other areas. The survey papers deal with both classical and abstract potential theory and its relations to partial differential equations, stochastic processes and other branches such as numerical analysis and topology. A collection of problems from potential theory, compiled on the occasion of the conference, is included, with additional commentaries, in the second part of this volume.

Sommaire:
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 Schr?;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.