Potential Theory, Surveys and Problems

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.