Author(s)

Abdelkrim Barbara, El Houcine Rami, Elhoussine Azroul

Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohammed Ben Abdellah University, Atlas Fez, Morocco.

We consider, for a bounded open domain Ω in Rⁿ and a function u : Ω → R^m, the quasilinear elliptic system: (1). We generalize the system (QES)_(f,g) in considering a right hand side depending on the jacobian matrix Du. Here, the star in (QES)_(f,g) indicates that f may depend on Du. In the right hand side, v belongs to the dual space W^-1,P’(Ω, ω^*, R^m), , f and g satisfy some standard continuity and growth conditions. We prove existence of a regularity, growth and coercivity conditions for σ, but with only very mild monotonicity assumptions.

Quasilinear Elliptic, Sobolev Spaces with Weight, Young Measure, Galerkin Scheme

Barbara, A. , Rami, E. and Azroul, E. (2021) Quasilinear Degenerated Elliptic Systems with Weighted in Divergence Form with Weak Monotonicity with General Data. Applied Mathematics, 12, 500-519. doi: 10.4236/am.2021.126035.