On boundary behavior of harmonic functions in Hölder domains
type: Item
instance of: scholarly article
title: On boundary behavior of harmonic functions in Hölder domains
zbMATH Open document ID: 0922.31005
DOI: 10.1007/BF02498219
author: Fausto Ferrari
published in: The Journal of Fourier Analysis and Applications
publication date: 1999-09-30T00:00:00Z
full work available at URL: https://eudml.org/doc/59576
review text: Let \(L\) denote a uniformly elliptic operator with bounded coefficients on a Hölder domain \(D\). Using probabilistic techniques, \textit{R. Bañuelos, R. F. Bass} and \textit{K. Burdzy} [Duke Math. J. 64, No. 1, 195-200 (1991; Zbl 0755.35027)] proved a boundary Harnack principle for \(L\)-harmonic functions on \(D\). In the paper under review, assuming that \(L\) has smooth coefficients, the author proves the same result by purely analytic methods; the estimates obtained do not depend on the smoothness of the coefficients. Results about \(L\)-harmonic measure on \(\partial D\) are also proved, notably a doubling property.
Mathematics Subject Classification ID: 31B25
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 1269731
zbMATH Keywords: uniformly elliptic operator
zbMATH Keywords: boundary Harnack principle
zbMATH Keywords: smooth coefficients
zbMATH Keywords: \(L\)-harmonic measure
reviewed by: D. H. Armitage
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1269731