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

Pavlov, G. A.

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.

MSC:

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

Keywords:

uniqueness; local existence; abstract inverse problem; locally convex spaces; topological vector spaces