Analyticity for solution of fractional integro-differential equations. (November 2022)

• Record Type: Journal Article
• Authors: Blatt, Simon
• Is Part Of: Nonlinear analysis. Volume 224(2022)
• Publication Date: 2022-11
• Subjects: 35A20 -- 35R11; Integro-differential equations -- Fractional Laplacian -- Non-linear elliptic equation -- Real analytic solutions -- Faá di Bruno's formula -- Method of majorants; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113071
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove that for a certain class of kernels K ( y ) viscosity solutions of the integro-differential equation ∫ R n ( u ( x + y ) − 2 u ( x ) + u ( x − y ) ) K ( y ) d y = f ( x, u ( x ) ) are locally analytic if f is an analytic function. This extends results in Albanese et al. (2015) in which it was shown that such solutions belong to certain Gevrey classes.