Existence of weak solutions for some quasilinear degenerated elliptic systems in weighted Sobolev spaces
DOI:
https://doi.org/10.22199/issn.0717-6279-5336Keywords:
quasilinear elliptic system, Young measure, Galerkin schemaAbstract
We consider, for a bounded open domain Ω in Rn; (n ≥ 1) and a function u : Ω → ℝm; (m ≥ 1) the quasilinear elliptic system:
(0.1)
Which is a Dirichlet problem. Here, v belongs to the dual space
, f and g satisfy some stan- dard continuity and growth conditions. we will show the existence of a weak solution of this problem in the four following cases: σ is mono- tonic, σ is strictly monotonic, σ is quasi montone and σ derives from a convex potential.
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