@Article{JPDE-27-1,
author = {Ouaro , Stanislas and Ouedraogo , Arouna},
title = {<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},
journal = {Journal of Partial Differential Equations},
year = {2014},
volume = {27},
number = {1},
pages = {1--27},
abstract = {<p>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.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v27.n1.1},
url = {http://global-sci.org/intro/article_detail/jpde/5123.html}
}