Well-Posed Problems for the Laplace Operator in a Punctured Disk
Matematičeskie zametki, Tome 89 (2011) no. 6, pp. 856-867.

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We give a complete description of well-posed solvable boundary-value problems for the Laplace operator in the disk and in the punctured disk. We present formulas for resolvents of well-posed problems for the Laplace operator in the disk.
Keywords: Laplace operator, well-posed solvable boundary-value problem, punctured disk, nonhomogeneous Laplace equation, Dirichlet boundary condition, Green function, Dirac function.
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B. E. Kanguzhin; A. A. Anijarov. Well-Posed Problems for the Laplace Operator in a Punctured Disk. Matematičeskie zametki, Tome 89 (2011) no. 6, pp. 856-867. http://geodesic.mathdoc.fr/item/MZM_2011_89_6_a5/

[1] R. L. De Kronig, W. G. Penney, “Quantum mechanics of electrons in crystal lattices”, Proc. R. Soc. Lond. A, 130:814 (1931), 499–513 | DOI | Zbl

[2] E. Fermi, “Sul moto dei neutroni nelle sostanze idrogenante”, Ric. Sci. Progr. Tecn. Econom. Naz., 2 (1936), 13–52 | Zbl

[3] F. A. Berezin, L. D. Faddeev, “Zamechanie ob uravnenii Shredingera s singulyarnym potentsialom”, Dokl. AN SSSR, 137:5 (1961), 1011–1014 | MR | Zbl

[4] S. Albeverio, R. Høegh-Krohn, F. Gesztesy, H. Holden, “Some exactly solvable models in quantum mechanics and the low energy expansions”, Proceedings of the Second International Conference on Operator Algebras, Ideals, and Their Applications in Theoretical Physics (Leipzig, 1983), Teubner-Texte Math., 67, Teubner, Leipzig, 1984 | MR | Zbl

[5] A. M. Savchuk, A. A. Shkalikov, “Operatory Shturma–Liuvillya s potentsialami-raspredeleniyami”, Tr. MMO, 64 (2003), 159–212 | MR | Zbl

[6] A. V. Bitsadze, Uravneniya matematicheskoi fiziki, Nauka, M., 1976 | MR | Zbl