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A strong type of regularity for the $\textrm {PWB}$ solution of the Dirichlet problem


Author: D. H. Armitage
Journal: Proc. Amer. Math. Soc. 61 (1976), 285-289
MSC: Primary 31B20
DOI: https://doi.org/10.1090/S0002-9939-1976-0427658-1
MathSciNet review: 0427658
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Abstract: Let ${H_f}$ be the Perron-Wiener-Brelot solution of the Dirichlet problem for a resolutive function $f$ on the boundary $\partial \Omega$ of a bounded domain $\Omega$ in ${E^n}$. A point $y$ of $\partial \Omega$ will be called strongly regular if ${H_f}(x) \to f(y)(x \to y)$ whenever $f$ is resolutive and continuous at $y$. Necessary and sufficient conditions for strong regularity are given.


References [Enhancements On Off] (What's this?)

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Keywords: Dirichlet problem, regular boundary point
Article copyright: © Copyright 1976 American Mathematical Society