Existence results of quasilinear elliptic systems via Young measures
نویسندگان
1 Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay slimane University, Morocco
2 Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay slimane University, Morocco
3 Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay slimane University, Morocco
4 Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay slimane University, Morocco
doi
10.22075/ijnaa.2022.26962.3463چکیده
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 $u\in W_{0}^{1,p}(\Omega;\mathbb{R}^{m})$.
