Publication at Faculty of Mathematics and Physics |
2008
Abstract
Concave functions in Potential Theory are defined by means of representing measures with respect to the space of functions continuous on the closure of an open set U and harmonic on U. It is proved that such concave functions are continuous on U and several characterizations of concave functions are given.
Most of the results are established in the context of harmonic spaces, covering solutions of elliptic and parabolic second order partial differential equations.