Analyticity for Solution of Integro-Differential Operators
Abstract
We prove that for a certain class of kernels K(y) that viscosity solutions of the integro-differential equation ∫ Rn (u(x+y) - 2 u(x) + u(x-y)) K(y) dy = f(x,u(x)) are locally analytic if f is an analytic function. This extends the result of Albanese, Fiscella, Valdinoci that such solutions belong to certain Gevrey classes.
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