Uniqueness of a solution of an abstract inverse problem. (English. Russian original) Zbl 0672.31009

Differ. Equations 24, No. 8, 917-920 (1988); translation from Differ. Uravn. 24, No. 8, 1402-1406 (1988).
Summary: The uniqueness and the local existence of the solution of an abstract inverse problem from potential theory is considered. The study is carried out for potentials defined in \(R^ n\) as well as in locally convex spaces with values in topological vector spaces, satisfying certain conditions. The potential is introduced for a family of (in general) nonlinear and multivalued operators.


31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
35R30 Inverse problems for PDEs
31C15 Potentials and capacities on other spaces