### 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

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