We prove for some singular kernels K(x, y) that viscosity solutions of the integro-differential equation. ∫Rn[u(x+y)+u(x-y)-2u(x)]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.
Albanese, G., Fiscella, A., Valdinoci, E. (2015). Gevrey regularity for integro-differential operators. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 428(2), 1225-1238 [10.1016/j.jmaa.2015.04.002].
Gevrey regularity for integro-differential operators
Fiscella, A
;
2015
Abstract
We prove for some singular kernels K(x, y) that viscosity solutions of the integro-differential equation. ∫Rn[u(x+y)+u(x-y)-2u(x)]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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