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

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

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 r...

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Veröffentlicht in:Nonlinear analysis 2018-10, Vol.175, p.173-190
Hauptverfasser: Abatangelo, Nicola, Jarohs, Sven, Saldaña, Alberto
Format: Artikel
Sprache:eng
Schlagworte:
[formula omitted]-harmonic functions
Boggio’s formula
Boundary value problems
Differential equations
Green's functions
Harmonic analysis
Harmonic functions
Laplace transforms
Maximum principles
Nonlinear systems
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Zusammenfassung: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2018.05.019