TY - JOUR T1 - L1 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 -

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.