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arXiv · 1504.00831

Gevrey regularity for integro-differential operators

Guglielmo Albanese·Alessio Fiscella·Enrico Valdinoci
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Abstract

We prove for some singular kernels $K(x,y)$ that viscosity solutions of the integro-differential equation $\int_{\mathbb{R}^n} \left[u(x+y)+u(x-y)-2u(x)\right]\,K(x,y)dy=f(x)$ locally belong to some Gevrey class if so does $f$. The fractional Laplacian equation is included in this framework as a special case.

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Guglielmo Albanese, Alessio Fiscella, Enrico Valdinoci. 2015-04-03. Gevrey regularity for integro-differential operators. https://doi.org/10.1016/j.jmaa.2015.04.002

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