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Intrinsic Hölder Continuity of Harmonic Functions.

Intrinsic Hölder Continuity of Harmonic Functions.

Authors :
Hansen, Wolfhard
Source :
Potential Analysis; Jul2017, Vol. 47 Issue 1, p1-12, 12p
Publication Year :
2017

Abstract

In a setting, where only 'exit measures' are given, as they are associated with a right continuous strong Markov process on a separable metric space, we provide simple criteria for scaling invariant Hölder continuity of bounded harmonic functions with respect to a distance function which, in applications, may be adapted to the special situation. In particular, already a very weak scaling property ensures that Harnack inequalities imply Hölder continuity. Our approach covers recent results by M. Kassmann and A. Mimica as well as cases, where a Green function leads to an intrinsic metric. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
09262601
Volume :
47
Issue :
1
Database :
Complementary Index
Journal :
Potential Analysis
Publication Type :
Academic Journal
Accession number :
123838060
Full Text :
https://doi.org/10.1007/s11118-016-9604-8