Some geometric properties for a class of non-Lipschitz domains. (English) Zbl 1066.35028

Summary: 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 \(\mathcal{C}\).


35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35B35 Stability in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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