Low regularity results for degenerate Poisson problems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914166791471104 |
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| author | Calanchi, Marta Grossi, Massimo |
| author_facet | Calanchi, Marta Grossi, Massimo |
| contents | In this paper we study the Poisson problem, \[ \begin{cases} -{\rm div}(d^β\nabla u)=f&{\rm in}\ Ω\\ u=0&{\rm on}\ \partialΩ, \end{cases} \] where $Ω\subset\mathbb R^N$, $N\ge2$ is a smooth bounded domain, $f$ is a continuous function, $β< 1$, and $d(x)=dist(x,\partialΩ)$. We describe the behaviour of $u$ near $\partialΩ$ and discuss some of its regularity properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low regularity results for degenerate Poisson problems Calanchi, Marta Grossi, Massimo Analysis of PDEs In this paper we study the Poisson problem, \[ \begin{cases} -{\rm div}(d^β\nabla u)=f&{\rm in}\ Ω\\ u=0&{\rm on}\ \partialΩ, \end{cases} \] where $Ω\subset\mathbb R^N$, $N\ge2$ is a smooth bounded domain, $f$ is a continuous function, $β< 1$, and $d(x)=dist(x,\partialΩ)$. We describe the behaviour of $u$ near $\partialΩ$ and discuss some of its regularity properties. |
| title | Low regularity results for degenerate Poisson problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.08649 |