Potential Theory Surveys and Problems: Proceedings of a Conference held in Prague, July 19–24, 1987

Alano Ancona (auth.), Josef Král, Jaroslav Lukeš, Ivan Netuka, Jiří Veselý (eds.)0387502106, 9780387502106

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.

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Table of contents :
Positive harmonic functions and hyperbolicity….Pages 1-23
Order and convexity in potential theory….Pages 24-41
Probability methods in potential theory….Pages 42-54
Layer potential methods for boundary value problems on lipschitz domains….Pages 55-80
Fine potential theory….Pages 81-97
Balayage spaces — A natural setting for potential theory….Pages 98-117
Axiomatic non-linear potential theories….Pages 118-132
Application of the potential theory to the study of qualitative properties of solutions of the elliptic and parabolic equations….Pages 133-153
Weighted extremal length and beppo levi functions….Pages 154-161
An introduction to iterative techniques for potential problems….Pages 162-180
Potential theory methods for higher order elliptic equations….Pages 181-195
Problems on distortion under conformal mappings….Pages 198-198
On the riesz representation of finely superharmonic functions….Pages 199-201
Nonlinear elliptic measures….Pages 202-204
Problems on a relation between measures and corresponding potentials….Pages 205-206
Open problems connected with level sets of harmonic functions….Pages 207-210
On the extremal boundary of convex compact measures which represent a non-regular point in choquet simplex….Pages 211-213
The problem of construction of the harmonic space based on choquet simplex….Pages 214-215
The problem on quasi-interior in choquet simplexes….Pages 216-219
Boundary regularity and potential-theoretic operators….Pages 220-222
Contractivity of the operator of the arithmetical mean….Pages 223-225
Fine maxima….Pages 226-228
Repeated singular integrals….Pages 229-230
Cofine potential theory….Pages 231-231
Essential and principal balayages….Pages 232-233
Local connectedness of the fine topology….Pages 234-235
On the lusin-menchoff property….Pages 236-237
Relations between parabolic capacities….Pages 238-239
Isovolumetric inequalities for the least harmonic majorant of |x| p ….Pages 240-241