Show simple item record

Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent

dc.creatorOuaro, Stanislas
dc.date2012-06-01
dc.identifierhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/1340
dc.identifier10.4067/S0719-06462012000200002
dc.descriptionWe study the existence and uniqueness of weak and entropy solutions for the nonlinear inhomogeneous Neumann boundary value problem involving the 𝑝(𝑥)-Laplace of the form − div ɑ(𝑥, ∇𝑢) + |𝑢| 𝑝(𝑥)−2 𝑢 = f in Ω, ɑ(𝑥, ∇𝑢).η = 𝜑 on ∂Ω, where Ω is a smooth bounded open domain in ℝN, N ≥ 3, 𝑝 ∈ C(Ω) and 𝑝(𝑥) > 1 for 𝑥 ∈ Ω. We prove the existence and uniqueness of a weak solution for data 𝜑 ∈ L(𝑝−) ′ (∂Ω) and f ∈ L(𝑝−) ′ (Ω), the existence and uniqueness of an entropy solution for L1−data f and 𝜑 independent of 𝑢 and the existence of weak solutions for f dependent on 𝑢 and 𝜑 ∈ L(𝑝−) ′ (Ω).en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/1340/1195
dc.sourceCUBO, A Mathematical Journal; Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal; 15–41en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 14 Núm. 2 (2012): CUBO, A Mathematical Journal; 15–41es-ES
dc.source0719-0646
dc.source0716-7776
dc.subjectGeneralized Lebesgue and Sobolev spacesen-US
dc.subjectWeak solutionen-US
dc.subjectEntropy solutionen-US
dc.subject𝑝(𝑥)-Laplace operatoren-US
dc.titleWeak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponenten-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


This item appears in the following Collection(s)

Show simple item record