The "hot spots" problem in planar domains with one hole

2004/05/25 by Krzysztof Burdzy, Burdzy, Krzysztof · 2 citations
Computer Science · Mathematics · #35P99 #60J65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #math.AP #math.PR #msc:35P99 #msc:60J65

paper · pdf · doi:10.48550/arxiv.math/0405472

arxiv created 2004/05/25 · openalex publication_date 2004/05/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.

Cited by

• Sharp bounds on the failure of the hot spots conjecture
• On hot-spots free subregions of convex domains

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