Existence and regularity of solutions to unilateral nonlinear elliptic equation in Marcinkiewicz space with variable exponent

Abstract

This manuscript proves the existence and regularity of solutions with respect to the summability of second member $g\in L^{m(\cdot)}(\Omega)$, to the obstacle problem associated to nonlinear elliptic equation \begin{equation} \left\{\begin{array}{lll}-\mbox{div}\>A(x,v,\nabla v)=g & \mbox{in} & \Omega, \\ u=0 & \mbox{in} & \partial\Omega. \end{array} \right. \end{equation} The arguments are based on the rearrangement techniques to obtain some priori estimates in Marcinkwicz spaces with variable exponents