A note on uniqueness for $L^1$-data elliptic problems with Orlicz growth
Volume 168 / 2022
Colloquium Mathematicum 168 (2022), 199-209
MSC: Primary 35J60; Secondary 35A01, 35A02.
DOI: 10.4064/cm8472-4-2021
Published online: 30 November 2021
Abstract
We study existence and uniqueness of solutions to the problem \[ -\mathop {\rm div} A(x,u,\nabla u) + g(x,u) = f\quad \ \text {in}\ \Omega \subset \mathbb R, \] where $\Omega $ is a bounded Lipschitz domain, $A$ has Orlicz growth with respect to the last two variables, $g$ satisfies the sign condition with respect to the second variable, and $f$ is merely integrable.
