%0 Journal Article 
%A Moussa, Hicham
%A Ortegón Gallego, Francisco
%A Rhoudaf, Mohamed
%T Capacity Solution to a Nonlinear Elliptic Coupled System in Orlicz–Sobolev Spaces
%D 2020
%@ 1660-5454
%U http://hdl.handle.net/10498/34096
%X We analyze the existence of a capacity solution to the following
nonlinear elliptic coupled system, whose unknowns are the temperature
inside a semiconductor material, u, and the electric potential, ϕ,
−Au = ρ(u)|∇ϕ|2 in Ω,
div(ρ(u)∇ϕ) = 0 in Ω,
ϕ = ϕ_0 on ∂Ω,
u = 0 on∂Ω,
where Ω ⊂ R^d, d ≥ 2 and Au = −div a(x, u,∇u) is a Leray–Lions operator defined on W^1_0 L_M(Ω), M is a N-function which does not have to satisfy a Δ_2 condition. Therefore, we work with generalized Orlicz–
Sobolev spaces which are not necessarily reflexive. The function ϕ_0 is given. The proof combines truncation methods, monotonicity techniques and regularizing methods in Orlicz spaces. We introduce a sequence of approximate problems which converges (up to a subsequence) in a certain sense to a capacity solution in the context of non-reflexive Orlicz–Sobolev spaces.
%K Coupled system
%K capacity solutions
%K nonlinear elliptic equations
%K weak solutions
%K Orlicz–Sobolev spaces
%~ Universidad de Cádiz