Gevrey regularity for integro-differential operators

Guglielmo Albanese; Alessio Fiscella; Enrico Valdinoci

doi:10.1016/j.jmaa.2015.04.002

Gevrey regularity for integro-differential operators

Guglielmo Albanese, Alessio Fiscella, Enrico Valdinoci

Research output: Contribution to journal › Article

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1225-1238
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	428
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.04.002
Publication status	Published - 1 Jan 2015
Externally published	Yes

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Albanese, G., Fiscella, A., & Valdinoci, E. (2015). Gevrey regularity for integro-differential operators. Journal of Mathematical Analysis and Applications, 428(2), 1225-1238. https://doi.org/10.1016/j.jmaa.2015.04.002

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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.",

keywords = "Fractional Laplacian, Gevrey class, Integro-differential equations",

author = "Guglielmo Albanese and Alessio Fiscella and Enrico Valdinoci",

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AU - Albanese, Guglielmo

AU - Fiscella, Alessio

AU - Valdinoci, Enrico

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Y1 - 2015/1/1

N2 - 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.

AB - 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.

KW - Fractional Laplacian

KW - Gevrey class

KW - Integro-differential equations

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