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.

Gevrey regularity for integro-differential operators / G. Albanese, A. Fiscella, E. Valdinoci. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 428:2(2015), pp. 1225-1238. [10.1016/j.jmaa.2015.04.002]

Gevrey regularity for integro-differential operators

G. Albanese
;
A. Fiscella
Secondo
;
E. Valdinoci
Ultimo
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.
Fractional Laplacian; Gevrey class; Integro-differential equations; Analysis; Applied Mathematics
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/472819
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