Asymptotics for the spectral heat function and bounds for integrals of Dirichlet eigenfunctions

DOI10.1017/S0308210500013172zbMath0938.58026OpenAlexW2764527253MaRDI QIDQ4267750

Simon P. Watson, Michiel van den Berg

Publication date: 14 June 2000

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500013172

zbMATH Keywords

asymptoticsheat kernelDirichlet eigenfunctions

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Perturbations of PDEs on manifolds; asymptotics (58J37)

Cites Work

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• Heat flow out of regions in \({\mathbb{R}}^ m\)
• Dirichlet-Neumann bracketing for horn-shaped regions
• Heat content asymptotics of a Riemannian manifold with boundary
• Heat flow and Brownian motion for a region in \({\mathbb{R}}^ 2\) with a polygonal boundary
• Über die asymptotische Verteilung der Eigenwerte des Laplace-Operators für Gebiete auf der Kugeloberfläche
• A Comparison Estimate for the Heat Equation with an Application to the Heat Content of the S -Adic Von Koch Snowflake
• Heat Content Asymptotics for Planar Regions with Cusps
• The Asymptotics of The Laplacian on a Manifold with Boundary

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