SMOOTHNESS OF SOLUTIONS TO NONLINEAR VARIATIONAL INEQUALITIES

Several questions about the smoothness of solutions to nonlinear variational inequalities with obstacles are studied. The method used is to consider the variational inequality as a multivalued equation involving a monotone graph. It is observed that the particular monotone graph with which the authors deal is also concave, leading to uniform bounds for second derivatives. These results are then applied to the variation of the function Au equals minus D//ia//i (Du).