Green function and Martin kernel for higher-order fractional Laplacians in balls. (October 2018)

• Record Type: Journal Article
• Authors: Abatangelo, Nicola; Jarohs, Sven; Saldaña, Alberto
• Is Part Of: Nonlinear analysis. Volume 175(2018)
• Page Start: 173
• Page End: 190
• Publication Date: 2018-10
• Subjects: 35C15 -- 35C04 -- 35S15 -- 35B50; Boggio's formula -- s-harmonic functions -- Maximum principles; 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.2018.05.019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We give the explicit formulas for the Green function and the Martin kernel for all integer and fractional powers of the Laplacian s > 1 in balls. As consequences, we deduce interior and boundary regularity estimates for solutions to linear problems and positivity preserving properties. Our proofs rely on a characterization of suitable s -harmonic functions and on a differential recurrence equation.