Harmonic measure and heat equation
type: Item
instance of: scholarly article
title: Harmonic measure and heat equation
zbMATH Open document ID: 0916.31001
DOI: 10.1007/BF02559511
author: Yanick Heurteaux
published in: Arkiv för Matematik
publication date: 1997-11-13T00:00:00Z
review text: It is shown that the harmonic measure \(\omega_p\) of \(E\subseteq\partial \Omega\) at \(P\in\Omega\) for the (heat) operator \(\frac{\partial}{\partial t}- \frac{\partial^2} {\partial x^2}\) is absolutely continuous with respect to the length measure on \(\partial \Omega\) for \(C'{}^\alpha\) functions [see also \textit{R. P. Kaufman} and \textit{J. M. Wu}, J. Differ. Equations 80, 14-31 (1989; Zbl 0678.35042); ibid. 43, 204-234 (1982; Zbl 0534.31005)].
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 896436
zbMATH Keywords: heat equation
zbMATH Keywords: absolute continuity
zbMATH Keywords: harmonic measure
reviewed by: S. K. Rangarajan
MaRDI profile type: Publication
cites work: A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations
cites work: Solutions positives et mesure harmonique pour des operateurs paraboliques dans des ouverts ``Lipschitziens''. (Positive solutions and harmonic measure for parabolic operators in ``Lipschitz'' domains)
cites work: Parabolic potential theory
cites work: Dirichlet problem of heat equation for \(C^ 2\) domains
cites work: Temperatures in Several Variables: Kernel Functions, Representations, and Parabolic Boundary Values
cites work: Regularity Properties of Commutators and Layer Potentials Associated to the Heat Equation
cites work: Q3475681
cites work: Uniqueness of positive solutions of the heat equation
cites work: Q5607484
cites work: A Hausdorff measure classification of polar sets for the heat equation
cites work: Q3756738
cites work: On Parabolic Measures and Subparabolic Functions
cites work: On heat capacity and parabolic measure
full work available at URL: https://doi.org/10.1007/bf02559511
OpenAlex ID: W2080748823
description: scientific article; zbMATH DE number 896436