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- Title
Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains.
- Authors
Ishige, Kazuhiro; Salani, Paolo; Takatsu, Asuka
- 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 The first (positive) Dirichlet eigenfunction of the Laplacian on a ball in H N raised to some power α > 0 is strictly concave; Let Γ be the heat kernel on H N . Then Γ (⋅ , y , t) is strictly log-concave in H N for y ∈ H N and t > 0.
- Subjects
SYMMETRIC domains; BOUNDARY value problems; RIEMANNIAN manifolds; HYPERBOLIC spaces; DIRICHLET problem
- Publication
Communications in Contemporary Mathematics, 2022, Vol 24, Issue 9, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199721500978