Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains

Ishige, K.; Salani, P.; Takatsu, A.

doi:10.1142/S0219199721500978

We study power concavity of rotationally symmetric solutions to elliptic and parabolic boundary value problems on rotationally symmetric domains in Riemannian manifolds. As applications of our results to the hyperbolic space H^N, we have: 1. The first (positive) Dirichlet eigenfunction of the Laplacian on a ball in H^N raised to some power α > 0 is strictly concave. 2. Let L be the heat kernel on H^N. Then L(⋅,y,t) is strictly log-concave in H^N for y H^N and t > 0.

Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains / Ishige K.; Salani P.; Takatsu A.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - (2021), pp. 0-0. [10.1142/S0219199721500978]

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Titolo:	Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains
Autori di Ateneo:	Ishige K. Salani P. Takatsu A. (Corresponding)
Autori:	Ishige K.; Salani P.; Takatsu A.
Anno di registrazione:	2021
Rivista:	COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
Pagina iniziale:	0
Pagina finale:	0
Abstract:	We study power concavity of rotationally symmetric solutions to elliptic and parabolic boundary value problems on rotationally symmetric domains in Riemannian manifolds. As applications of our results to the hyperbolic space H^N, we have: 1. The first (positive) Dirichlet eigenfunction of the Laplacian on a ball in H^N raised to some power α > 0 is strictly concave. 2. Let L be the heat kernel on H^N. Then L(⋅,y,t) is strictly log-concave in H^N for y H^N and t > 0.
Handle:	http://hdl.handle.net/2158/1253714
Appare nelle tipologie:	1a - Articolo su rivista

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