Luis Silvestre, Holder estimates for solutions of integro differential equations like the fractional laplace, Indiana Univ. Math. J. 55 (2006), 1155-1174
Abstract
We provide 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. Our assumptions include the case of an operator with variable order, without any continuity assumption in that order.
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