On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet Laplacian

DOI10.1016/0022-1236(87)90005-XzbMath0632.35016MaRDI QIDQ1095307

Michiel van den Berg

Publication date: 1987

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

spectrumtraceheat kernelFeynman-Kac formulaDirichlet Laplacianpointwise estimatesEuler's constantAsymptotic resultsregular boundarydiagonal elements

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Heat equation (35K05) General theory of partial differential operators (47F05)

Related Items (24)

The geometric invariants for the spectrum of the Stokes operator ⋮ Heat content estimates over sets of finite perimeter ⋮ Spectral invariants of the perturbed polyharmonic Steklov problem ⋮ On traces associated with the Dirichlet Laplacian ⋮ Heat flow out of regions in \({\mathbb{R}}^ m\) ⋮ Trace estimates for unimodal Lévy processes ⋮ Refined asymptotic expansion for the partition function of unbounded quantum billiards ⋮ Uniform stability of the Dirichlet spectrum for rough outer perturbations ⋮ Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain ⋮ Trace estimates for relativistic stable processes ⋮ Dirichlet-Neumann bracketing for horn-shaped regions ⋮ Trace estimates for stable processes ⋮ The Trace of the Heat Kernel in Lipschitz Domains ⋮ Heat content for stable processes in domains of \(\mathbb {R}^d\) ⋮ Heat content and small time asymptotics for Schrödinger operators on \(\mathbb R^d\) ⋮ Two-term trace estimates for relativistic stable processes ⋮ Unnamed Item ⋮ Heat equation and the principle of not feeling the boundary ⋮ Unnamed Item ⋮ Efficiency and localisation for the first Dirichlet eigenfunction ⋮ On the trace of symmetric stable processes on Lipschitz domains ⋮ Equivalent descriptions of the Loewner energy ⋮ Uniform bounds for the heat content of open sets in Euclidean space ⋮ Asymptotic expansion of the trace of the heat kernel associated to the Dirichlet-to-Neumann operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonclassical eigenvalue asymptotics
• Trace properties of the Dirichlet Laplacian
• The asymptotics of the heat equation for a boundary value problem
• On the spectrum of the Dirichlet Laplacian for Horn-shaped regions in \(R^ n\) with infinite volume
• Curvature and the eigenvalues of the Laplacian
• Trace Properties of Some Highly Anisotropic Operators
• Heat Kernel Bounds for Second Order Elliptic Operators on Riemannian Manifolds
• Bounds on Green’s functions of second-order differential equations
• The asymptotic distribution of eigenvalues of the Laplace operator in an unbounded domain
• Can One Hear the Shape of a Drum?
• ON THE EIGENVALUES OF THE FIRST BOUNDARY VALUE PROBLEM IN UNBOUNDED DOMAINS
• On Spectra of Second-Order Differential Operators

This page was built for publication: On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet Laplacian