Inverse problems for elliptic equations in the space: II

We consider inverse problems of finding the right-hand side of a linear second-order elliptic equation of general form. The first boundary value problem is studied. We consider two ways of indicating additional information (overdetermination): the trace of the solution can be given on some lower-dimensional manifold inside the domain, or the normal derivative can be specified on part of the boundary. On the basis of the Fredholm alternative proved in the first part of the present paper for the inverse problems in question, we single out conditions on the given functions under which the inverse problem is uniquely solvable. Various types of such conditions are considered. The study is carried out in the class of continuous functions whose derivatives satisfy the Hölder condition.