T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

El Houssine Azroul, et al. "T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum." Applicationes Mathematicae 39.3 (2012): 339-364. <http://eudml.org/doc/279953>.

@article{ElHoussineAzroul2012,
abstract = {We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem $-div(a(x,u,∇u)) + g(x,u) = f - divF$ in Ω, where Ω is a bounded open domain of $ℝ^\{N\}$, N ≥ 2 and $a: Ω × ℝ× ℝ^\{N\} → ℝ^\{N\}$ is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to $∏_\{i=1\}^\{N\}L^\{p^\{\prime \}(·)\}(Ω)$.},
author = {El Houssine Azroul, Abdelkrim Barbara, Meryem El Lekhlifi, Mohamed Rhoudaf},
journal = {Applicationes Mathematicae},
keywords = {Sobolev spaces with variable exponent; truncations; nonlinear elliptic equations; Minty lemma},
language = {eng},
number = {3},
pages = {339-364},
title = {T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum},
url = {http://eudml.org/doc/279953},
volume = {39},
year = {2012},
}

TY - JOUR
AU - El Houssine Azroul
AU - Abdelkrim Barbara
AU - Meryem El Lekhlifi
AU - Mohamed Rhoudaf
TI - T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 3
SP - 339
EP - 364
AB - We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem $-div(a(x,u,∇u)) + g(x,u) = f - divF$ in Ω, where Ω is a bounded open domain of $ℝ^{N}$, N ≥ 2 and $a: Ω × ℝ× ℝ^{N} → ℝ^{N}$ is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to $∏_{i=1}^{N}L^{p^{\prime }(·)}(Ω)$.
LA - eng
KW - Sobolev spaces with variable exponent; truncations; nonlinear elliptic equations; Minty lemma
UR - http://eudml.org/doc/279953
ER -