Measure Data for a General Class of Nonlinear Elliptic Problems

Mohammed El Ansari; Youssef Akdim; Soumia Lalaoui Rhali

Measure Data for a General Class of Nonlinear Elliptic Problems

Analysis of PDEs 2023-08-03 v1

Authors: Mohammed El Ansari , Youssef Akdim , Soumia Lalaoui Rhali

Abstract

We consider nonlinear elliptic inclusion having a measure in the right-hand side of the type $\beta(u)-div a(x,Du)\ni \mu$ in $\Omega$ a bounded domain in $\mathbb{R}^{N},$ with $\beta$ is a maximal monotone graph in $\mathbb{R}^2$ and $a(x,Du)$ is a Leray-Lions type operator. We study a suitable notion of solution for this kind of problem. The functional setting involves anisotropic Sobolev spaces.

Keywords

positive solutions of elliptic equations elliptic partial differential equations semilinear elliptic equations

Cite

@article{arxiv.2308.01122,
  title  = {Measure Data for a General Class of Nonlinear Elliptic Problems},
  author = {Mohammed El Ansari and Youssef Akdim and Soumia Lalaoui Rhali},
  journal= {arXiv preprint arXiv:2308.01122},
  year   = {2023}
}

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