Some geometric properties for a class of non-Lipschitz domains

Abstract:

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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mohammed.barkatou@ramq.gouv.qc.ca