Potential Theory, Surveys and Problems

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.

Contenu
Positive harmonic functions and hyperbolicity.- Order and convexity in potential theory.- Probability methods in potential theory.- Layer potential methods for boundary value problems on lipschitz domains.- Fine potential theory.- Balayage spaces A natural setting for potential theory.- Axiomatic non-linear potential theories.- Application of the potential theory to the study of qualitative properties of solutions of the elliptic and parabolic equations.- Weighted extremal length and beppo levi functions.- An introduction to iterative techniques for potential problems.- Potential theory methods for higher order elliptic equations.- Problems on distortion under conformal mappings.- On the riesz representation of finely superharmonic functions.- Nonlinear elliptic measures.- Problems on a relation between measures and corresponding potentials.- Open problems connected with level sets of harmonic functions.- On the extremal boundary of convex compact measures which represent a non-regular point in choquet simplex.- The problem of construction of the harmonic space based on choquet simplex.- The problem on quasi-interior in choquet simplexes.- Boundary regularity and potential-theoretic operators.- Contractivity of the operator of the arithmetical mean.- Fine maxima.- Repeated singular integrals.- Cofine potential theory.- Essential and principal balayages.- Local connectedness of the fine topology.- On the lusin-menchoff property.- Relations between parabolic capacities.- Isovolumetric inequalities for the least harmonic majorant of |x|p.