Hasnae El Hammar, Said Ait Temghart, Chakir Allalou, Said Melliani
abstract:
In this paper, we study the existence of weak solutions for some quasilinear
elliptic problems with perturbed gradients under homogeneous Dirichlet boundary
conditions. Using the approximate Galerkin method and combining the convergence
in terms of Young measure and the theory of Sobolev spaces, we can prove that
there is at least one weak solution $u\in W_{0}^{1,p(x)}(\Omega;\mathbb{R}^{m})$
to the problem treated.
Mathematics Subject Classification: 35J60, 35D05, 76A05
Key words and phrases: Quasilinear elliptic systems, approximate Galerkin method, Young measures