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
\[\begin{cases}
-\operatorname{div}(a(|D u|) D u)= f(x,u,Du) \qquad \text { in }\; \Omega \\
u =0 \qquad \qquad\;\qquad\qquad\qquad\;\;\qquad\text { on }\; \;\partial \Omega,
\end{cases}\]
where $\Omega$ 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 $u\in W_{0}^{1,p}(\Omega;\mathbb{R}^{m})$.

Keywords

• Quasilinear elliptic systems
• Weak solutions
• Young measures