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]
Titolo: | Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains | |
Autori di Ateneo: | Takatsu A. (Corresponding) | |
Autori: | Ishige K.; Salani P.; Takatsu A. | |
Anno di registrazione: | 2021 | |
Rivista: | ||
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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