On the error in the two-term Weyl formula for the Dirichlet Laplacian

DOI10.1063/1.5145003zbMath1458.35142arXiv2001.01876OpenAlexW3100489677MaRDI QIDQ3298917

Rupert L. Frank, Simon Larson

Publication date: 16 July 2020

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.01876

zbMATH Keywords

eigenvalue asymptoticsRiesz meansDirichlet Laplaciantrace of the heat kernel

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Heat kernel (35K08)

Related Items (3)

Introduction to the Special Issue: In memory of Jean Bourgain ⋮ The Lieb–Thirring inequalities: Recent results and open problems ⋮ Semiclassical asymptotics for a class of singular Schrödinger operators

Cites Work

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• Can one hear the dimension of a fractal?
• Estimation of the remainder in the Weyl formula
• Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain
• Curvature and the eigenvalues of the Laplacian
• The Trace of the Heat Kernel in Lipschitz Domains
• Heat Equation for a Region in R² with a Polygonal Boundary
• Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture
• A heat trace anomaly on polygons
• Can One Hear the Shape of a Drum?
• ON THE EIGENVALUES OF THE FIRST BOUNDARY VALUE PROBLEM IN UNBOUNDED DOMAINS

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