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arXiv · 2406.04773

Uniform estimates for a family of Poisson problems: `rounding off the corners'

Benoît Daniel·Simon Labrunie·Victor Nistor
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Abstract

We prove \emph{uniform solvability estimates} for certain families of elliptic problems posed in a bounded family of domains (for example, a sequence that converges to another domain). We provide uniform estimates both in weighted and in usual Sobolev spaces. When the limit domain is a \emph{polygon} and the other domains are smooth, our results amount to rounding off'' the corners of the limit domain. The technique of proof is based on a suitable conformal modification of the metric, which makes the union of the domains a manifold with boundary and relative bounded geometry.

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Benoît Daniel, Simon Labrunie, Victor Nistor. 2024-06-07. Uniform estimates for a family of Poisson problems: `rounding off the corners'. https://arxiv.org/abs/2406.04773

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