This manuscript proves the existence and regularity of solutions with
respect to the summability of second member 1 ? Lm(?)(?), to the obstacle
problem associated to nonlinear elliptic equation (?div A(x, v,?v) = g in
?, u = 0 in ??. (1) The arguments are based on the rearrangement techniques
to obtain some priori estimates in Marcinkwicz spaces with variable
exponents.