Existence of solutions for a quasilinear elliptic system with variable exponent

Document Type : Research Paper

Authors

1 Departement of Mathematics Faculte of Sciences Sidi Mohamed Ben Abdellah University Dhar Mehraz Fez Morocco

2 University of Sidi Mohamed Ben Abdellah Faculty of Sciences Dhar El Mehraz

10.22075/ijnaa.2019.18418.2011

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