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arXiv · 2308.01122

Measure Data for a General Class of Nonlinear Elliptic Problems

Mohammed El Ansari·Youssef Akdim·Soumia Lalaoui Rhali
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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.

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Mohammed El Ansari, Youssef Akdim, Soumia Lalaoui Rhali. 2023-08-02. Measure Data for a General Class of Nonlinear Elliptic Problems. https://arxiv.org/abs/2308.01122

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