Intrinsic Hölder continuity of harmonic functions
نویسنده
چکیده
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.
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Weak reverse Hölder inequality of weakly A-harmonic sensors and Hölder continuity of A-harmonic sensors
* Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China Abstract In this paper, we obtain the weak reverse Hölder inequality of weakly A-harmonic sensors and establish the Hölder continuity of A-harmonic sensors. Mathematics Subject Classification 2010: 58A10 · 35J60
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