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Bibliographic Details
Main Authors: Della Pietra, Francesco, di Blasio, Giuseppina, Radice, Teresa
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.10607
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Table of Contents:
  • 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.