The Trace of the Heat Kernel in Lipschitz Domains

DOI10.2307/2154304zbMath0853.35083OpenAlexW4238066962MaRDI QIDQ3142103

Russell M. Brown

Publication date: 5 January 1997

Full work available at URL: https://doi.org/10.2307/2154304

zbMATH Keywords

asymptotic expansiontrace 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)

Related Items

Two-term spectral asymptotics for the Dirichlet pseudo-relativistic kinetic energy operator on a bounded domain ⋮ Global Existence of Solutions to Reaction-Diffusion Systems with Mass Transport Type Boundary Conditions ⋮ Trace estimates for unimodal Lévy processes ⋮ Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain ⋮ Trace estimates for relativistic stable processes ⋮ A PDE approach to a 2-dimensional matching problem ⋮ On the error in the two-term Weyl formula for the Dirichlet Laplacian ⋮ Trace estimates for stable processes ⋮ On the trace of symmetric stable processes on Lipschitz domains ⋮ Finer estimates on the \(2\)-dimensional matching problem ⋮ One can hear the shape of ellipses of small eccentricity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonclassical eigenvalue asymptotics
• Can one hear the dimension of a fractal?
• On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet Laplacian
• Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
• A sharp asymptotic remainder estimate for the eigenvalues of the Laplacian in a domain of \(R^3\)
• On the spectrum of the Dirichlet Laplacian for Horn-shaped regions in \(R^ n\) with infinite volume
• Removal of the log factor in the asymptotic estimates of polygonal membrane eigenvalues
• Curvature and the eigenvalues of the Laplacian
• The Initial-Neumann Problem for the Heat Equation in Lipschitz Cylinders
• 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
• Can One Hear the Shape of a Drum?
• A harnack inequality for parabolic differential equations