INVERSE COEFFICIENT PROBLEMS FOR MONOTONE POTENTIAL-OPERATORS

In this paper the class of inverse coefficient problems for nonlinear monotone potential elliptic operators is considered. This class is cha racterized by the property that the coefficient of elliptic operator d epends on the gradient of the solution, i.e. on xi = /del u/(2). The u nknown coefficient k = k(xi) is required to belong to a set of admissi ble coefficients which is compact in H-1(0, xi) Using a variational a pproach to the nonlinear direct problem it is shown that the solution u((n)) of the linearized direct problem converges to the solution of t he nonlinear direct problem in H-1-norm. For the nonlinear direct prob lem weak H-1-coefficient convergence is proved. This result allows one to prove the existence of quasisolutions of inverse problems with dif ferent types of additional conditions (measured data). As an important application of the theory, an inverse elastoplastic problem for a cyl indrical bar and a nonlinear Sturm-Liouville problem are considered.