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 |
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| container_title | Nonlinear analysis |
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| creator | Abatangelo, Nicola Jarohs, Sven Saldaña, Alberto |
| description | 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. |
| doi_str_mv | 10.1016/j.na.2018.05.019 |
| format | Article |
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| ispartof | Nonlinear analysis, 2018-10, Vol.175, p.173-190 |
| issn | 0362-546X 1873-5215 |
| language | eng |
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| source | Access via ScienceDirect (Elsevier) |
| subjects | [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 |
| title | Green function and Martin kernel for higher-order fractional Laplacians in balls |
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