<em>L</em><sup>1</sup> Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent
Year: 2014
Author: Stanislas Ouaro, Arouna Ouedraogo
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 1 : pp. 1–27
Abstract
In this work, we study the following nonlinear homogeneous Neumann boundary value problem $β(u)−diva(x,∇u) ∋ f in Ω, a(x,∇u)⋅η$ $=0$ on $∂Ω$, where $Ω$ is a smooth bounded open domain in $ℜ^N, N ≥ 3$ with smooth boundary $∂Ω$ and $η$ the outer unit normal vector on $∂Ω$. We prove the existence and uniqueness of an entropy solution for L¹-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v27.n1.1
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 1 : pp. 1–27
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Elliptic equation