On a multidimensional integral equation with data supported by low-dimensional analytic manifolds

Abstract

Abstract. This paper is concerned with a 3D linear integral equation of the first kind which arises when solving nonlinear coefficient inverse problems for second order hyperbolic PDEs. We prove that the integral equation has at most one solution when its right part is given on appropriate analytic 2D and 1D manifolds. As compared to known uniqueness theorems, the dimension of a smooth manifold supporting problem data is decreased here from four to one. As auxiliary results, we give examples of 1D analytic manifolds of uniqueness and examples of minimal countable sets of uniqueness for harmonic functions in 3D domains.