Document Type : Research Paper

Authors

• Hasnae El Hammar
• Said Ait Temghart
• Chakir Allalou
• Said Melliani

Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay slimane University, Morocco

Abstract

This paper is concerned with the following quasilinear elliptic system
$$\{\begin{array}{l}-\mathrm{div}(a(|Du|)Du)=f(x,u,Du)\text{ in }\mathrm{\Omega }\\ u=0\text{ on }\partial \mathrm{\Omega },\end{array}$$
where $\mathrm{\Omega }$ is a bounded open subset of ${\mathbb{R}}^n$. By means of the Young measure and the theory of Sobolev spaces, we obtain the existence of a weak solution $u\in W_0^{1,p}(\mathrm{\Omega };{\mathbb{R}}^m)$.

Keywords

• Quasilinear elliptic systems
• Weak solutions
• Young measures