TY - JOUR
T1 - <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
AU - Ouaro , Stanislas
AU - Ouedraogo , Arouna
JO - Journal of Partial Differential Equations
VL - 1
SP - 1
EP - 27
PY - 2014
DA - 2014/03
SN - 27
DO - http://doi.org/10.4208/jpde.v27.n1.1
UR - https://global-sci.org/intro/article_detail/jpde/5123.html
KW - Elliptic equation
KW - variable exponent
KW - entropy solution
KW - L¹-data
KW - Neumann boundary condition
AB - <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>