@misc{10498/34096,
year = {2020},
month = {2},
url = {http://hdl.handle.net/10498/34096},
abstract = {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.},
organization = {Ministerio de Ciencia, Innovación y Universidades (TEC2017-86347-C2-1-R) con la participación del Fondo Europeo de Desarrollo Regional (FEDER).},
publisher = {Springer},
keywords = {Coupled system},
keywords = {capacity solutions},
keywords = {nonlinear elliptic equations},
keywords = {weak solutions},
keywords = {Orlicz–Sobolev spaces},
title = {Capacity Solution to a Nonlinear Elliptic Coupled System in Orlicz–Sobolev Spaces},
doi = {10.1007/s00009-020-1485-9},
author = {Moussa, Hicham and Ortegón Gallego, Francisco and Rhoudaf, Mohamed},
}