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 Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 1, Pages 109–137 (Mi izv2125)

Green function properties and generalized solutions of elliptic boundary value problems

Yu. P. Krasovskii

Abstract: We consider the properties of the Green functions of general boundary value problems for elliptic equations and the properties following from them of the adjoints of the resolvents. The results obtained are used to study generalized solutions. We prove existence and estimate theorems for generalized solutions in spaces that are the negatives of Höder spaces.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:1, 105–130

Bibliographic databases:

UDC: 517.9
MSC: 35J25, 35D05

Citation: Yu. P. Krasovskii, “Green function properties and generalized solutions of elliptic boundary value problems”, Izv. Akad. Nauk SSSR Ser. Mat., 33:1 (1969), 109–137; Math. USSR-Izv., 3:1 (1969), 105–130

Citation in format AMSBIB
\Bibitem{Kra69} \by Yu.~P.~Krasovskii \paper Green function properties and generalized solutions of elliptic boundary value problems \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1969 \vol 33 \issue 1 \pages 109--137 \mathnet{http://mi.mathnet.ru/izv2125} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=244611} \zmath{https://zbmath.org/?q=an:0169.13203|0192.45301} \transl \jour Math. USSR-Izv. \yr 1969 \vol 3 \issue 1 \pages 105--130 \crossref{https://doi.org/10.1070/IM1969v003n01ABEH000750} 

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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. Ya. A. Roitberg, “Homeomorphism theorems and a Green's formula for general elliptic boundary problems with nonnormal boundary conditions”, Math. USSR-Sb., 12:2 (1970), 177–212
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. Lopushanskaya G.P., “Generalized boundary value problems for semilinear elliptic equations in weighted function spaces”, Differ. Equ., 45:12 (2009), 1757–1768
4. M. Yu. Zaslavskii, “On interpretation of the direct current electrical prospecting measurements”, Math. Models Comput. Simul., 3:1 (2011), 9–17
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