Holder estimates for solutions of integro differential equations like the fractional laplace Luis Silvestre 45K0560J7535B65integro-differential equationsnonlocal equationsH"older estimatesjump processes We provide a purely analytical proof of H\"older 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. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2706 10.1512/iumj.2006.55.2706 en Indiana Univ. Math. J. 55 (2006) 1155 - 1174 state-of-the-art mathematics http://iumj.org/access/