| Abstract: |
| 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 $\Omega\subset R^N$, $N\ge2$ 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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