@Article{JPDE-27-1, author = {Ouaro , Stanislas and Ouedraogo , Arouna}, title = {L1 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 = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n1.1}, url = {http://global-sci.org/intro/article_detail/jpde/5123.html} }