Abstract:
This article is a study of the Dirichlet problem
{Lu=0inΩ,∂αu|∂Ω=0,|α|⩽m−1,
where Ω⊂Rn is an open (possibly unbounded) set,
α=(α1,…,αn) is a multi-index,
|α|=α1+⋯+αn,
L=∑|α|=|β|=m∂α(aαβ(x)∂β),
and the coefficients aαβ(x) are N×N matrices.
Citation:
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
\Bibitem{Kon93}
\by A.~A.~Kon'kov
\paper On the dimension of the~solution space of elliptic systems in unbounded domains
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 80
\issue 2
\pages 411--434
\mathnet{http://mi.mathnet.ru/eng/sm1030}
\crossref{https://doi.org/10.1070/SM1995v080n02ABEH003531}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1254803}
\zmath{https://zbmath.org/?q=an:0832.35038}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995QR47400008}
Linking options:
https://www.mathnet.ru/eng/sm1030
https://doi.org/10.1070/SM1995v080n02ABEH003531
https://www.mathnet.ru/eng/sm/v184/i12/p23
This publication is cited in the following 23 articles:
V. V. Brovkin, “Solvability of the Neumann problem for the p-Laplacian on manifolds with a model end”, Moscow University Mathematics Bulletin, 79:3 (2024), 103–111
S. M. Bakiev, A. A. Kon'kov, “On the Existence of Solutions of the Dirichlet Problem for the p-Laplacian on Riemannian Manifolds”, Math. Notes, 114:5 (2023), 679–686
V. V. Brovkin, “On the Existence of Solutions of the Neumann Problem for the p-Laplacian on Parabolic Manifolds with a Model End”, Diff Equat, 59:1 (2023), 29
V. V. Brovkin, A. A. Kon'kov, “Existence of Solutions to the Second Boundary-Value Problem for the p-Laplacian on Riemannian Manifolds”, Math. Notes, 109:2 (2021), 171–183
Hovik A. Matevossian, “Mixed biharmonic Dirichlet–Neumann problem in exterior domains”, Zhurn. SFU. Ser. Matem. i fiz., 13:6 (2020), 755–762
Matevossian H.A., “On the Mixed Neumann-Robin Problem For the Elasticity System in Exterior Domains”, Russ. J. Math. Phys., 27:2 (2020), 272–276
Matevossian H.A., “On the Polyharmonic Neumann Problem in Weighted Spaces”, Complex Var. Elliptic Equ., 64:1 (2019), 1–7
O. A. Matevosyan, “Bigarmonicheskaya zadacha Dirikhle–Farviga vo vneshnikh oblastyakh”, Sib. elektron. matem. izv., 16 (2019), 1716–1731
Matevossian H.A., “Mixed Boundary Value Problems For the Elasticity System in Exterior Domains”, Math. Comput. Appl., 24:2 (2019), UNSP 58
Matevossian H., “On the Mixed Dirichlet-Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces”, Math. Comput. Appl., 24:1 (2019), UNSP 25
Hovik Matevossian, “On the Mixed Steklov—Neumann and Steklov-type Biharmonic Problems in Unbounded Domains”, IOP Conf. Ser.: Mater. Sci. Eng., 683:1 (2019), 012016
H. A. Matevossian, “On the Steklov-Type Biharmonic Problem in Unbounded Domains”, Russ. J. Math. Phys., 25:2 (2018), 271
H. A. Matevossian, “On the biharmonic Steklov problem in weighted spaces”, Russ. J. Math. Phys., 24:1 (2017), 134
Matevosyan O.A., “On solutions of a boundary value problem for the biharmonic equation”, Differ. Equ., 52:10 (2016), 1379–1383
H. A. Matevossian, “Mixed Dirichlet–Steklov problem for the biharmonic equation in weighted spaces”, J. Math. Sci. (N. Y.), 234:4 (2018), 440–454
S. F. Chichoyan, “Smoothness of Solutions of the Dirichlet Problem for the Biharmonic Equation in Nonsmooth 2D Domains”, Math. Notes, 98:6 (2015), 999–1001
H. A. Matevossian, “On Solutions of the Neumann Problem for the Biharmonic Equation in Unbounded Domains”, Math. Notes, 98:6 (2015), 990–994
A. L. Beklaryan, “On the Existence of Solutions of the First Boundary-Value Problem for Elliptic Systems of High Order in Unbounded Domains”, Math. Notes, 96:2 (2014), 290–293
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
Beklaryan A.L., “On the Existence of Solutions of the First Boundary Value Problem for Elliptic Equations on Unbounded Domains”, Russ. J. Math. Phys., 19:4 (2012), 509–510
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