Abstract:
We select a class of uniqueness of the solutions
of the quasi-elliptic
equation with the Dirichlet condition on the boundary of an unbounded domain
Ω⊂Rn+1 and show that for domains with irregular
behaviour of the boundary this class can be wider than that established
in [10] for second-order elliptic equations. For the Laplace equation
we construct an example of non-uniqueness of solution of the Dirichlet
problem that shows that the class of uniqueness found in this paper cannot be
essentially extended.
Citation:
L. M. Kozhevnikova, “Anisotropic classes of uniqueness of the solution of the Dirichlet
problem for quasi-elliptic equations”, Izv. Math., 70:6 (2006), 1165–1200
\Bibitem{Koz06}
\by L.~M.~Kozhevnikova
\paper Anisotropic classes of uniqueness of the solution of the Dirichlet
problem for quasi-elliptic equations
\jour Izv. Math.
\yr 2006
\vol 70
\issue 6
\pages 1165--1200
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\crossref{https://doi.org/10.1070/IM2006v070n06ABEH002342}
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Linking options:
https://www.mathnet.ru/eng/im716
https://doi.org/10.1070/IM2006v070n06ABEH002342
https://www.mathnet.ru/eng/im/v70/i6/p93
This publication is cited in the following 7 articles:
L. M. Kozhevnikova, A. A. Khadzhi, “Existence of solutions of anisotropic elliptic equations with nonpolynomial nonlinearities in unbounded domains”, Sb. Math., 206:8 (2015), 1123–1149
V. F. Gilimshina, F. Kh. Mukminov, “On the decay of solutions of non-uniformly elliptic equations”, Izv. Math., 75:1 (2011), 53–71
I. M. Bikkulov, F. Kh. Mukminov, “Klassy edinstvennosti resheniya zadachi Rikke dlya ellipticheskikh uravnenii chetvertogo i shestogo poryadkov”, Ufimsk. matem. zhurn., 2:1 (2010), 35–51
R. Kh. Karimov, L. M. Kozhevnikova, “Povedenie na beskonechnosti reshenii kvazilineinykh ellipticheskikh uravnenii vtorogo poryadka v neogranichennykh oblastyakh”, Ufimsk. matem. zhurn., 2:2 (2010), 53–66
L. M. Kozhevnikova, “O suschestvovanii i edinstvennosti reshenii zadachi Dirikhle dlya psevdodifferentsialnykh ellipticheskikh uravnenii v oblastyakh s nekompaktnymi granitsami”, Ufimsk. matem. zhurn., 1:1 (2009), 38–68
A. R. Gerfanov, F. Kh. Mukminov, “Shirokii klass edinstvennosti resheniya dlya neravnomerno ellipticheskogo uravneniya v neogranichennoi oblasti”, Ufimsk. matem. zhurn., 1:3 (2009), 11–27
L. M. Kozhevnikova, “Behaviour at infinity of solutions of pseudodifferential
elliptic equations in unbounded domains”, Sb. Math., 199:8 (2008), 1169–1200
Citation in format AMSBIB
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