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Existence and regularity results for nonlinear and nonhomogeneous elliptic equation

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Abstract

We study the existence and regularity of solutions for the nonlinear elliptic problem

$$\begin{aligned} \left\{ \begin{array}{lll} -\text{ div }\>a(x,u,\nabla u)=f &{}\text{ in }&{} \varOmega ,\\ u=0 &{}\text{ on } &{}\partial \varOmega , \end{array}\right. \end{aligned}$$

where \(\varOmega \) is a bounded open set in \({\mathbf {R}}^N, (N\ge 2),\) a a Carathéodory function, and f in \(L^{m(\cdot )}(\varOmega ).\)

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  1. Faculty of Sciences Dhar El Mahraz, Laboratory LAMA, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Aharrouch Benali & Bennouna Jaouad

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  1. Aharrouch Benali
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  2. Bennouna Jaouad
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Correspondence to Aharrouch Benali.

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Benali, A., Jaouad, B. Existence and regularity results for nonlinear and nonhomogeneous elliptic equation. J Elliptic Parabol Equ 7, 961–975 (2021). https://doi.org/10.1007/s41808-021-00121-0

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  • DOI: https://doi.org/10.1007/s41808-021-00121-0

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