Existence results of quasilinear elliptic systems via Young measures

Document Type : Research Paper


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


This paper is concerned with the following quasilinear elliptic system
-\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,
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 $u\in W_{0}^{1,p}(\Omega;\mathbb{R}^{m})$.


Volume 14, Issue 1
January 2023
Pages 1111-1123
  • Receive Date: 24 April 2022
  • Revise Date: 10 August 2022
  • Accept Date: 13 September 2022