Geodesic
Young measure theory for steady problems in Orlicz-Sobolev spaces
Novi Sad Journal of Mathematics, Tome 53 (2023) no. 1.

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In this paper, we study the existence of weak solutions for Dirichlet boundary-value problems given in the following quasilinear elliptic system \[\left\{ \begin{array}{rl} -\text{div}\,\sigma(x,u,Du)+b(x,u,Du)=f(x,u,Du)\quad\text{in}\;\Omega,\\ u=0\quad\text{on}\;\partial\Omega. \end{array} \right.\] We prove the needed result, relying on the theory of Young measures, Galerkin's approximation and weak monotonicity assumptions on $\sigma$, in reflexive Orlicz-Sobolev spaces.
Publié le :
DOI : 10.30755/NSJOM.12610
Classification : 35J57, 35D30, 46E30
Keywords: Orlicz–Sobolev spaces, Quasilinear elliptic systems, Young measures 
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Elhoussine Azroul; Farah Balaadich. Young measure theory for steady problems in Orlicz-Sobolev spaces. Novi Sad Journal of Mathematics, Tome 53 (2023) no. 1. doi : 10.30755/NSJOM.12610. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.12610/

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