We deal with nonnegative functions satisfying where s ∈(0, 1) and C is a given cone on ℝn with vertex at zero. We consider the case when s approaches 1, wondering whether solutions of the problem do converge to harmonic functions in the same cone or not. Surprisingly, the answer will depend on the opening of the cone through an auxiliary eigenvalue problem on the upper half-sphere. These conic functions are involved in the study of the nodal regions in the case of optimal partitions and other free boundary problems and play a crucial role in the extension of the Alt-Caffarelli-Friedman monotonicity formula to the case of fractional diffusions

Terracini, S., Tortone, G., Vita, S. (2018). On s-Harmonic functions on cones. ANALYSIS & PDE, 11(7), 1653-1691 [10.2140/apde.2018.11.1653].

On s-Harmonic functions on cones

Terracini, S;Vita, S
2018

Abstract

We deal with nonnegative functions satisfying where s ∈(0, 1) and C is a given cone on ℝn with vertex at zero. We consider the case when s approaches 1, wondering whether solutions of the problem do converge to harmonic functions in the same cone or not. Surprisingly, the answer will depend on the opening of the cone through an auxiliary eigenvalue problem on the upper half-sphere. These conic functions are involved in the study of the nodal regions in the case of optimal partitions and other free boundary problems and play a crucial role in the extension of the Alt-Caffarelli-Friedman monotonicity formula to the case of fractional diffusions
Articolo in rivista - Articolo scientifico
Asymptotic behavior; Conic functions; Fractional Laplacian; Martin kernel; Analysis; Numerical Analysis; Applied Mathematics
English
2018
11
7
1653
1691
none
Terracini, S., Tortone, G., Vita, S. (2018). On s-Harmonic functions on cones. ANALYSIS & PDE, 11(7), 1653-1691 [10.2140/apde.2018.11.1653].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/229456
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