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Hölder estimates for solutions of integro-differential equations like the fractional Laplace. (English) Zbl 1101.45004
The author provides a purely analytical proof of Hölder continuity for harmonic functions with respect to a class of integro-differential equations like the ones associated with purely jump processes. The assumptions on the operator are more flexible than in previous works. The assumptions include the case of an operator with variable order, without any continuity assumption in that order.

MSC:
45K05 Integro-partial differential equations
60J75 Jump processes (MSC2010)
35B65 Smoothness and regularity of solutions to PDEs
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