An Inverse Problem for a Quasilinear Elliptic Equation

Abstract

We consider the inverse problem for a quasilinear second order elliptic equation with the unknown coefficient at the lower-order term and the first kind boundary condition and the integral overedetermination condition on the boundary. We prove a theorem on the local existence and uniqueness of a strong solution to the problem. The result is illustrated by an example of a nonlinear equation satisfying all the assumptions of the theorem. Bibliography: 6 titles.