Uniform estimates for a family of Poisson problems: `rounding off the corners'
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929412519231488 |
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| author | Daniel, Benoît Labrunie, Simon Nistor, Victor |
| author_facet | Daniel, Benoît Labrunie, Simon Nistor, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04773 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform estimates for a family of Poisson problems: `rounding off the corners' Daniel, Benoît Labrunie, Simon Nistor, Victor Analysis of PDEs Differential Geometry 35R01, 35J15, 46E35, 58J32 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. |
| title | Uniform estimates for a family of Poisson problems: `rounding off the corners' |
| topic | Analysis of PDEs Differential Geometry 35R01, 35J15, 46E35, 58J32 |
| url | https://arxiv.org/abs/2406.04773 |