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Jensen measures in potential theory

Authors
  • Hansen, Wolfhard
  • Netuka, Ivan
Type
Preprint
Publication Date
Jul 08, 2010
Submission Date
Jul 08, 2010
Identifiers
arXiv ID: 1007.1311
Source
arXiv
License
Yellow
External links

Abstract

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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