Analyticity for Solution of Integro-Differential Operators

Simon Blatt

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arXiv · 2009.07673

Analyticity for Solution of Integro-Differential Operators

Simon Blatt

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Abstract

We prove that for a certain class of kernels $K(y)$ that viscosity solutions of the integro-differential equation $$ \int_{\mathbb R^n} (u(x+y) - 2 u(x) + u(x-y)) K(y) dy = f(x,u(x)) $$ 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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Simon Blatt. 2020-09-16. Analyticity for Solution of Integro-Differential Operators. https://arxiv.org/abs/2009.07673

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