Existence of solutions for a quasilinear elliptic system with variable exponent

نویسندگان
Azroul, Elhoussine ID 1
Balaadich, Farah ID 2

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

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

doi
10.22075/ijnaa.2019.18418.2011
چکیده

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.

کلیدواژه‌ها
Quasilinear elliptic systems, Sobolev spaces with variable exponent, Weak solutions, Young measures