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New York Journal of Mathematics 8 (2002), 189-213.

Some geometric properties for a class of non-Lipschitz domains

Mohammed Barkatou

Published: November 21, 2002
Keywords: convergence of domains, normal cone, Sobolev capacity, stability of the Dirichlet problem, Steiner symmetrization, Wiener criterion
Subject: 35J05, 51A05 and 52A20


In this paper, we introduce a class $\mathcal{C}$, of domains of $\mathbb{R}^{N}$, $N\geq 2$, which satisfy a geometric property of the inward normal (such domains are not Lipschitz, in general). We begin by giving various results concerning this property, and we show the stability of the solution of the Dirichlet problem when the domain varies in $\mathcal{C}$.

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