preprint

Inserted: 18 oct 2026

Year: 2024

Abstract:

In this paper, we study the existence and the summability of solutions to a Robin boundary value problem whose prototype is the following: $$ \begin{cases} -\text{div}(b(
u
)\nabla u)=f &\text{in }Ω,\\.2cm \displaystyle\frac{\partial u}{\partial ν}+βu=0 &\text{on }\partialΩ\end{cases} $$ where $Ω$ is a bounded Lipschitz domain in $\mathbb R^N$, $N>2$, $β>0$, $b(s)$ 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.