Back to Search
Start Over
On a nonlinear Robin problem with an absorption term on the boundary and $L^1$ data
- Publication Year :
- 2023
-
Abstract
- We deal with existence and uniqueness of nonnegative solutions to \begin{equation*} \left\{ \begin{array}{l} -\Delta u = f(x) \text{ in }\Omega, \frac{\partial u}{\partial \nu} + \lambda(x) u = \frac{g(x)}{u^\eta} \text{ on } \partial\Omega, \end{array} \right. \end{equation*} where $\eta\ge 0$ and $f,\lambda$ and $g$ are nonnegative integrable functions. The set $\Omega\subset\mathbb{R}^N (N> 2)$ is open and bounded with smooth boundary and $\nu$ denotes its unit outward normal vector. More generally, we handle equations driven by monotone operators of $p$-Laplacian type jointly with nonlinear boundary conditions. We prove existence of an entropy solution and check that this solution is unique under natural assumptions. Among other features, we study the regularizing effect given to the solution by both the absorption and the nonlinear boundary term.
- Subjects :
- Mathematics - Analysis of PDEs
35J25, 35J60, 35J70, 35J75, 35A01, 35A02
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2303.17232
- Document Type :
- Working Paper