Abstract Mixed Boundary-Value and Spectral Conjugation Problems and their Applications

Abstract

Based on the abstract Green formula, we study a general approach to abstract boundary value conjugation problems. We consider examples of some configurations of docked domains for conjugation problems, using the generalized Green formula for the Laplace operator. Also, we consider spectral problems with two complex parameters: one of them can be treated as a fixed one, while the other can be treated as the spectral one. By means of the proposed general approach, we reduce those problems to the spectral problem for operator bundles with self-adjoint operator coefficients acting in Hilbert space and depending on two parameters.