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.
Abatangelo N., Jarohs S., Saldana A. (2018). Green function and Martin kernel for higher-order fractional Laplacians in balls. NONLINEAR ANALYSIS, 175, 173-190 [10.1016/j.na.2018.05.019].
Green function and Martin kernel for higher-order fractional Laplacians in balls
Abatangelo N.;
2018
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.File in questo prodotto:
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