INVERSE COEFFICIENT PROBLEMS FOR ELLIPTIC VARIATIONAL-INEQUALITIES WITH A NONLINEAR MONOTONE OPERATOR

The class of inverse problems for a nonlinear elliptic variational ine quality is considered. The nonlinear elliptic operator is assumed to b e a monotone potential. The unknown coefficient of the operator depend s on the gradient of the solution and belongs to a set of admissible c oefficients which is compact in H-1(0, xi). It is shown that the nonl inear operator is pseudomonotone for the given class of coefficients. For the corresponding direct problem H-1- coefficient convergence is p roved. Based on this result the existence of a quasisolution of the in verse problem is obtained. As an important application an inverse diag nostic problem for an axially symmetric elasto-plastic body is conside red. For this problem the numerical method and computational results a re also presented.