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arXiv · 2503.08649

Low regularity results for degenerate Poisson problems

Marta Calanchi·Massimo Grossi
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Abstract

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.

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Marta Calanchi, Massimo Grossi. 2025-11-22. Low regularity results for degenerate Poisson problems. https://arxiv.org/abs/2503.08649

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