Special Session 123: Nonlinear phenomena in elliptic and parabolic equations

LOW REGULARITY RESULTS FOR DEGENERATE POISSON PROBLEMS
Marta Calanchi
Universit\`a degli Studi di Milano
Italy
Co-Author(s):    M. GROSSI
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.