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 Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 5, Pages 977–1010 (Mi izv2572)

Isolation of singularities of the Green's function

Yu. P. Krasovskii

Abstract: A method is given for constructing the Green's function for general boundary-value problems for elliptic equations. Pointwise estimates are proved for the Green's function in a closed region. A representation of an arbitrary solution of the boundary-value problem is derived, which permits the explicit construction of the irregular part of the solution if the latter contains singularities.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:5, 935–966

Bibliographic databases:

UDC: 517.9
MSC: 35A20, 35J25

Citation: Yu. P. Krasovskii, “Isolation of singularities of the Green's function”, Izv. Akad. Nauk SSSR Ser. Mat., 31:5 (1967), 977–1010; Math. USSR-Izv., 1:5 (1967), 935–966

Citation in format AMSBIB
\Bibitem{Kra67} \by Yu.~P.~Krasovskii \paper Isolation of singularities of the Green's function \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1967 \vol 31 \issue 5 \pages 977--1010 \mathnet{http://mi.mathnet.ru/izv2572} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=223740} \zmath{https://zbmath.org/?q=an:0153.42701|0174.15703} \transl \jour Math. USSR-Izv. \yr 1967 \vol 1 \issue 5 \pages 935--966 \crossref{https://doi.org/10.1070/IM1967v001n05ABEH000594} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. P. Krasovskii, “Green function properties and generalized solutions of elliptic boundary value problems”, Math. USSR-Izv., 3:1 (1969), 105–130
2. Yu. P. Krasovskii, “Differential properties of solutions of elliptic boundary-value problems with power singularities on the right-hand sides”, Math. USSR-Izv., 5:1 (1971), 211–219
3. S. D. Ivasishen, “Green's matrices of boundary value problems for Petrovskii parabolic systems of general form. I”, Math. USSR-Sb., 42:1 (1982), 93–144
4. S. D. Ivasishen, “Green's matrices of boundary value problems for Petrovskii parabolic systems of general form. II”, Math. USSR-Sb., 42:4 (1982), 461–498
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