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Green function and Martin kernel for higher-order fractional Laplacians in balls

par Abatangelo, Nicola ;Jarohs, Sven;Saldaña, Alberto
Référence Nonlinear analysis, 175, page (173-190)
Publication Publié, 2018-10-01

Article révisé par les pairs

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Résumé :

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.