Eventual concavity properties of the heat flow-Reference-Cited by-同舟云学术

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Eventual concavity properties of the heat flow

Published:2024-05-29 Issue: Volume: Page:
ISSN:0025-5831
Container-title:Mathematische Annalen
language:en
Short-container-title:Math. Ann.

Author:

Ishige Kazuhiro^ORCID

Abstract

AbstractThe eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of the eventual concavity properties of the heat flow for nonnegative, bounded measurable initial functions with compact support.

Funder

JSPS KAKENHI

The University of Tokyo

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s00208-024-02896-8.pdf

Reference31 articles.

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3. Brascamp, H.J., Lieb, E.H.: On extensions of the Brunn–Minkowski and Prékopa–Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. J. Funct. Anal. 22, 366–389 (1976)

4. Brigati, G., Dolbeault, J., Simonov, N.: Stability of the logarithmic Sobolev inequality. Preprint arXiv:2303.12926

5. Bénilan, P., VüLazquez, J.L.: Concavity of solutions of the porous medium equation. Trans. Am. Math. Soc. 299, 81–93 (1987)

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