The obstacle problem for nonlinear elliptic equations with variable   growth and L^1-data
  The aim of this paper is twofold: to prove, for L^1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy--Stampacchia inequalities to the general framework of L^1. 
Jos\'e Francisco Rodrigues, Manel Sanch\'on and Jos\'e Miguel Urbano