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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 5, Pages 1179–1199 (Mi izv2582)  

This article is cited in 9 scientific papers (total in 9 papers)

The solution of the first boundary-value problem for self-adjoint elliptic equations in the case of an unbounded region

L. D. Kudryavtsev


Abstract: In this paper we solve the first boundary-value problem for a self-adjoint second order elliptic equation in the case of an unbounded region in a certain class of functions, which is defined in a natural way by the equation itself. Existence and uniqueness theorem are proved by means of a variational method.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:5, 1131–1151

Bibliographic databases:

UDC: 517.9
MSC: 35J25, 47B25, 35A07, 35J20
Received: 26.11.1966

Citation: L. D. Kudryavtsev, “The solution of the first boundary-value problem for self-adjoint elliptic equations in the case of an unbounded region”, Izv. Akad. Nauk SSSR Ser. Mat., 31:5 (1967), 1179–1199; Math. USSR-Izv., 1:5 (1967), 1131–1151

Citation in format AMSBIB
\Bibitem{Kud67}
\by L.~D.~Kudryavtsev
\paper The solution of the first boundary-value problem for self-adjoint elliptic equations in the case of an unbounded region
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 5
\pages 1179--1199
\mathnet{http://mi.mathnet.ru/izv2582}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=217433}
\zmath{https://zbmath.org/?q=an:0174.15702|0153.42603}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 5
\pages 1131--1151
\crossref{https://doi.org/10.1070/IM1967v001n05ABEH000605}


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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. L. A. Bagirov, “Elliptic equations in unbounded domains”, Math. USSR-Sb., 15:1 (1971), 121–140  mathnet  crossref  mathscinet  zmath
    2. Rainer Janßen, “Elliptic Problems on Unbounded Domains”, SIAM J Math Anal, 17:6 (1986), 1370  crossref  mathscinet  zmath  isi
    3. A. A. Kon'kov, “On the dimension of the solution space of elliptic systems in unbounded domains”, Russian Acad. Sci. Sb. Math., 80:2 (1995), 411–434  mathnet  crossref  mathscinet  zmath  isi
    4. H. Matevossian, “The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral”, Math. Notes, 70:3 (2001), 363–377  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. H. Matevossian, “Solutions of exterior boundary-value problems for the elasticity system in weighted spaces”, Sb. Math., 192:12 (2001), 1763–1798  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. H. Matevossian, “On solutions of mixed boundary-value problems for the elasticity system in unbounded domains”, Izv. Math., 67:5 (2003), 895–929  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. O. A. Matevosyan, “Solutions of the Robin problem for the system of elastic theory in external domains”, J. Math. Sci. (N. Y.), 197:3 (2014), 367–394  mathnet  crossref  elib
    8. H. A. Matevossian, “On Solutions of the Neumann Problem for the Biharmonic Equation in Unbounded Domains”, Math. Notes, 98:6 (2015), 990–994  mathnet  crossref  crossref  mathscinet  isi  elib
    9. Matevosyan O.A., “Solution of a Mixed Boundary Value Problem For the Biharmonic Equation With Finite Weighted Dirichlet Integral”, Differ. Equ., 51:4 (2015), 487–501  mathnet  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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