Existence results of quasilinear elliptic systems via Young measures

This paper is concerned with the following quasilinear elliptic system\[\begin{cases}-\operatorname{div}(a(|D u|) D u)= f(x,u,Du) \qquad \text { in }\; \Omega \\u =۰ \qquad \qquad\;\qquad\qquad\qquad\;\;\qquad\text { on }\; \;\partial \Omega,\end{cases}\]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_{۰}^{۱,p}(\Omega;\mathbb{R}^{m}).

Keywords:

Quasilinear elliptic systems , Weak solutions , Young measures