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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, \[ \begin{cases} -{\rm div}(d^\beta\nabla u)=f&{\rm in}\ \Omega\\ u=0&{\rm on}\ \partial\Omega, \end{cases} \] where $\Omega\subset\mathbb R^N$, $N\ge2$ is a smooth bounded domain, $f$ is a continuous function, $\beta< 1$, and $d(x)=dist(x,\partial\Omega )$. We describe the behaviour of $u$ near $\partial\Omega$ and discuss some of its regularity properties.

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Marta Calanchi, Massimo Grossi. 2025-03-11. Low regularity results for degenerate Poisson problems. https://arxiv.org/abs/2503.08649

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