ON THE SOLUTION OF THE ILL-POSED CAUCHY PROBLEM FOR ELLIPTIC SYSTEMS OF THE FIRST ORDER

Abstract

In this paper, we consider the problem of recovering solutions of matrix factorizations
of the Helmholtz equation in a four-dimensional bounded domain from their values on a
part of the boundary of this domain, i.e., the Cauchy problem. Based on the Carleman function,
an explicit solution of the Cauchy problem for matrix factorizations of the Helmholtz equation
is constructed.