Duality theorems in some overdetermined boundary value problems

Abstract

Abstract We consider several elliptic boundary value problems for which there is an overspecification of data on the boundary of the domain. After reformulating the problems in an equivalent integral form, we use the alternate integral formulation to deduce that if a solution exists, then the domain must be an N ‐ball. Various Green's functions and classical boundary value problems of second, fourth and higher order are included among the problems considered here.