Strongly quasilinear elliptic systems with perturbations through yong measures

Abstract

We use the Galerkin method to obtain weak solutions for strongly quasilinear elliptic systems in the Sobolev space W^1,p₀(Ω; ℝ^m) of the form Gϖ(x) = f(x,ϖ,Dϖ) in Ω, with ϖ(x) = 0 on ∂Ω, where the term Gϖ(x) includes perturbations. Our approach involves the use of Young measures to obtain the desired results.