Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains

DOI10.1016/0022-1236(89)90118-3zbMath0676.60073OpenAlexW1971779315MaRDI QIDQ1122874

Burgess Davis, Rodrigo Bañuelos

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0022-1236(89)90118-3

zbMATH Keywords

heat equation with Dirichlet boundary condition

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Brownian motion (60J65)

Related Items (23)

Erratum: Sharp estimates for Dirichlet eigenfunctions in Horn-shaped regions ⋮ Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations ⋮ The lifetime of conditioned diffusions associated with some degenerate elliptic operators ⋮ The Generalized Diffusion Phenomenon and Applications ⋮ Brownian motion in twisted domains ⋮ Semismall perturbations in the Martin theory for elliptic equations ⋮ The influence of a power law drift on the exit time of Brownian motion from a half-line ⋮ Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries ⋮ Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian ⋮ The σ‐evolution equations with friction and unbounded coefficients ⋮ Diffusion phenomenon in Hilbert spaces and applications ⋮ Asymptotics for the heat kernel in multicone domains ⋮ Intrinsic ultracontractivity and the Dirichlet Laplacian ⋮ Intrinsic ultracontractivity and eigenfunction estimates for Schrödinger operators ⋮ On positive harmonic functions in cones and cylinders ⋮ Lifetimes of conditioned diffusions ⋮ Intrinsic ultracontractivity and small perturbation for one-dimensional generalized diffusion operators ⋮ Hitting times for special patterns in the symmetric exclusion process on \(\mathbb{Z}^d\) ⋮ A Conformal Inequality Related to the Conditional Gauge Theorem ⋮ Towards optimal gradient bounds for the torsion function in the plane ⋮ On the conditional expectation of the first exit time of Brownian motion ⋮ Ratio limit theorems for a Brownian motion killed at the boundary of a Benedicks domain ⋮ Ultracontractivity for Markov Semigroups and Quasi-Stationary Distributions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• The lifetime of conditioned Brownian motion in certain Lipschitz domains
• On an estimate of Cranston and McConnell for elliptic diffusions in uniform domains
• Doob's conditioned diffusions and their lifetimes
• The equivalence of certain heat kernel and Green function bounds
• The h-path distribution of the lifetime of conditioned Brownian motion for non-smooth domains
• Brownian motion and harnack inequality for Schrödinger operators
• On the principal eigenvalue of second-order elliptic differential operators
• The lifetime of conditioned Brownian motion
• Conditioned Brownian motion in planar domains

This page was built for publication: Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains