A note on hot-spots free subregions of convex domains

Fuente: arXiv
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Autor principal: Rohleder, Jonathan
Formato: Preprint
Publicado: 2025
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author Rohleder, Jonathan
author_facet Rohleder, Jonathan
contents The second eigenfunction of the Neumann Laplacian on convex, planar domains is considered. Inspired by the famous hot spots conjecture and a related result of Steinerberger, we show that potential critical points of this eigenfunction (and, in particular, interior ''hot spots'') cannot be located ''near the center'' of the domain. The region in which critical points are excluded is described explicitly.
format Preprint
id arxiv_https___arxiv_org_abs_2506_22184
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A note on hot-spots free subregions of convex domains
Rohleder, Jonathan
Analysis of PDEs
Mathematical Physics
Spectral Theory
The second eigenfunction of the Neumann Laplacian on convex, planar domains is considered. Inspired by the famous hot spots conjecture and a related result of Steinerberger, we show that potential critical points of this eigenfunction (and, in particular, interior ''hot spots'') cannot be located ''near the center'' of the domain. The region in which critical points are excluded is described explicitly.
title A note on hot-spots free subregions of convex domains
topic Analysis of PDEs
Mathematical Physics
Spectral Theory
url https://arxiv.org/abs/2506.22184