A note on quasilinear elliptic systems with $L^\infty$-data

F. Balaadich ; E. Azroul

Eurasian mathematical journal, Tome 14 (2023) no. 1, pp. 16-24

Résumé

We prove the existence of a weak energy solution for the boundary value problem \begin{eqnarray*} -\mathrm{div}\, a(x, u, Du) = f \text{ in } \Omega,\\ u = 0 \text{ on } \partial\Omega, \end{eqnarray*} where $\Omega$ is a smooth bounded open domain in $\mathbb{R}^n$ ($n\geqslant 3$) and $f\in L^\infty(\Omega;\mathbb{R}^m)$. The existence result is proved using the concept of Young measures.