On an inverse boundary-value problem for a second-order elliptic equation with non-classical boundary conditions

Abstract

An inverse boundary value problem for a second-order elliptic equation with periodic andintegral condition is investigated. The problem is considered in a rectangular domain. Toinvestigate the solvability of the inverse problem, we perform a conversion from the originalproblem to some auxiliary inverse problem with trivial boundary conditions. By thecontraction mapping principle we prove the existence and uniqueness of solutions of theauxiliary problem. Then we make a conversion to the stated problem again and, as a result,we obtain the solvability of the inverse problem.