In this paper, we study the existence and the summability of solutions to a Robin boundary value problem whose prototype is the following: $$ \begin{ cases} -\text{ div}(b(|u|)\nabla u)=f &\text{ in }\Omega,\\[.2cm] \displaystyle\frac{ \partial u}{ \partial \nu}+\beta u=0 &\text{ on }\partial\Omega \end{ cases} $$ where $\Omega$ is a bounded Lipschitz domain in $\mathbb R^N$, $N>2$, $\beta>0$, $b(s)$ is a positive function which may vanish at infinity and $f$ belongs to a suitable Lebesgue space. The presence of such a function $b$ in the principal part of the operator prevents it from being uniformly elliptic when $u$ is large.
Categories: math.AP