Neumann problem with a discontinuous nonlinearity
Analysis of PDEs
2026-04-28 v1 Functional Analysis
Abstract
This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we aim to derive an estimate that proves the well-posedness of the problem. This estimate serves as an evidence for the uniqueness of the existing solution when the boundary term is ``smooth".
Cite
@article{arxiv.2603.18732,
title = {Neumann problem with a discontinuous nonlinearity},
author = {Debajyoti Choudhuri and Dušan D. Repovš and Kamel Saoudi},
journal= {arXiv preprint arXiv:2603.18732},
year = {2026}
}