An Inverse Spectral Problem W.R.T. Domain

Анотація

Various practical problems, especially on hydrodynamics, elasticity theory, geophysics and aerodynamics, can be reduced to finding an optimal shape of a domain and studying its functionals.
In the paper, the inverse problem with respect to (w.r.t.) domain for two-dimensional Schrödinger operator and operator $L=\Delta^2$ is considered. The definition of s-functions is introduced. The method of determination of the domain by a given set of functions is proposed.
The main idea of the paper is to use a one-to-one correspondence between the convex bounded domains and their support functions and express the variation of the domain by the variation of corresponding support function.

Mathematics Subject Classification: 31B20, 49N45, 35R30, 65N21.