Green function and Martin kernel for higher-order fractional Laplacians in balls. (October 2018) - Abatangelo, Nicola; Jarohs, Sven; Saldaña, Alberto
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.