In this paper we study the Poisson problem, \[ \begin{cases} -{\rm div}(d^\beta\nabla u)=f&{\rm in}\ \Om\\ u=0&{\rm on}\ \partial\Omega, \end{cases} \] where $\Om\subset\R^N$, $N\ge2$ 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 $\partial\Om$ and discuss some of its regularity properties.
Low regularity results for degenerate Poisson problems / M. Calanchi, M. Grossi. - (2025 Mar 11).
Low regularity results for degenerate Poisson problems
M. Calanchi;
2025
Abstract
In this paper we study the Poisson problem, \[ \begin{cases} -{\rm div}(d^\beta\nabla u)=f&{\rm in}\ \Om\\ u=0&{\rm on}\ \partial\Omega, \end{cases} \] where $\Om\subset\R^N$, $N\ge2$ 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 $\partial\Om$ and discuss some of its regularity properties.
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