  Different practical problems, espesially, problems of hydrodynamics,
elasticity theory, geophysics and aerodynamics can be reduced to finding of an
optimal shape. The investigation of these problems is based on the study of
depending domain of the functiuonals their first variation and gradient.
  In the paper the inverse problem relatively domain is considered for
two-dimensional Schrodinger operator and operator and the definition of
functiuons is introduced. The method is proposed for for the determination of
the domain by given set of functions.
