On the stability of the solutions of inverse problems for elliptic equations

The inverse problems on finding the unknown lower coefficient in linear and nonlinear second-order elliptic equations with integral overdetermination conditions are considered. The conditions of overdetermination are given on the boundary of the domain. The continuous dependence of the strong solution on the input data of the inverse problem for the linear equation is proved in the case of the mixed boundary condition. As to the nonlinear equation, the continuous dependence of the strong solution on the overdetermination data is established for the inverse problem with the Dirichlet boundary condition.