The hot spots conjecture can be false: some numerical examples

DOI10.1007/s10444-021-09911-5zbMath1487.35204arXiv2101.01210OpenAlexW3118946389WikidataQ113904634 ScholiaQ113904634MaRDI QIDQ824322

Andreas Kleefeld

Publication date: 15 December 2021

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.01210

zbMATH Keywords

potential theoryboundary integral equationsHelmholtz equationnumericsinterior Neumann eigenvalues

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Boundary value problems for second-order elliptic equations (35J25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38)

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The hot spots conjecture can be false: some numerical examples ⋮ Improved upper bounds for the hot spots constant of Lipschitz domains ⋮ An upper bound on the hot spots constant ⋮ A spectral Galerkin exponential Euler time-stepping scheme for parabolic SPDEs on two-dimensional domains with a \(\mathcal{C}^2\) boundary

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