Geodesic
Abstract mixed boundary-value and spectral conjugation problems and their applications
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 61 (2016), pp. 67-102

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Basing on the abstract Green formula, we study general approach to abstract boundary-value conjugation problems. We consider examples of some configurations of docked domains for conjugation problems using generalized Green formula for the Laplace operator. Also we consider spectral problems with two complex parameters: one of them can be treated as fixed and the other one as spectral. By means of the proposed general approach, we reduce these problems to the spectral problem for operator pencil with self-adjoint operator coefficients acting in Hilbert space and depending on two parameters. 
@article{CMFD_2016_61_a2,
     author = {N. D. Kopachevskii and K. A. Radomirskaya},
     title = {Abstract mixed boundary-value and spectral conjugation problems and their applications},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {67--102},
     publisher = {mathdoc},
     volume = {61},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2016_61_a2/}
}
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N. D. Kopachevskii; K. A. Radomirskaya. Abstract mixed boundary-value and spectral conjugation problems and their applications. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 61 (2016), pp. 67-102. http://geodesic.mathdoc.fr/item/CMFD_2016_61_a2/