Jensen measures in potential theory

Details Jensen measures in potential theory Jensen measures in potential theory

2010-07-08

arxiv.org/abs/1007.1311v1

Mathematics

Analysis of PDEs

Scientific paper

It is shown that, for open sets in classical potential theory and - more generally - for elliptic harmonic spaces, the set of Jensen measures for a point is a simple union of closed faces of a compact convex set which has been thoroughly studied a long time ago. In particular, the set of extreme Jensen measures can be immediately identified. The results hold even without ellipticity (thus capturing also many examples for the heat equation) provided a rather weak approximation property for superharmonic functions or a certain transience property holds.

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