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Proceedings of the American Mathematical Society

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A strong type of regularity for the $ {\rm 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.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0427658-1
Keywords: Dirichlet problem, regular boundary point
Article copyright: © Copyright 1976 American Mathematical Society