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Hölder continuity of harmonic functions with respect to operators of variable order. (English) Zbl 1087.45004
The authors consider a class of integrodifferential operators and their corresponding harmonic functions. Under mild assumptions on the family of jump measures they prove a priori estimates and establish Hölder continuity of bounded functions that are harmonic in domain. Continuity estimates for harmonic functions have a long history, both in analysis and in probability.

MSC:
45K05 Integro-partial differential equations
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
35B65 Smoothness and regularity of solutions to PDEs
60J75 Jump processes (MSC2010)
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