L1 Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent (Journal of Partial Differential Equations, 2014)
"In this work, we study the following nonlinear homogeneous Neumann boundary value problem $\u03b2(u)\u2212diva(x,\u2207u) \u220b f in \u03a9, a(x,\u2207u)\u22c5\u03b7$ $=0$ on $\u2202\u03a9$, where $\u03a9$ is a smooth bounded open domain in $\u211c^N, N \u2265 3$ with smooth boundary $\u2202\u03a9$ and $\u03b7$ the outer unit normal vector on $\u2202\u03a9$. We prove the existence and uniqueness of an entropy solution for L\u00b9-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent."
Keywords: Elliptic equation; variable exponent; entropy solution; L¹-data; Neumann boundary condition