Existence of solutions for a quasilinear elliptic system with variable exponent

Document Type : Research Paper

Authors

University of Sidi Mohamed Ben Abdellah, Faculty of Sciences Dhar El Mehraz, B.P. 1796 Atlas, Fez, Morocco

Abstract

We consider the following quasilinear elliptic system in a Sobolev space with variable exponent:
\[-\text{div}(a(|Du|)Du)=f,\]
where $a$ is a $C^1$-function and $f\in W^{-1,p'(x)}(\Omega;\R^m)$. We use the theory of Young measures and weak monotonicity conditions to obtain the existence of solutions.

Keywords