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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 6, Pages 93–128 (Mi izv716)  

This article is cited in 7 scientific papers (total in 7 papers)

Anisotropic classes of uniqueness of the solution of the Dirichlet problem for quasi-elliptic equations

L. M. Kozhevnikova

Sterlitamak State Pedagogical Institute

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 $\Omega\subset\mathbb R^{n+1}$ 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.

DOI: https://doi.org/10.4213/im716

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English version:
Izvestiya: Mathematics, 2006, 70:6, 1165–1200

Bibliographic databases:

UDC: 517.956.4
MSC: 35A05, 35B45, 35K15, 35K30, 35K50, 35K65
Received: 23.05.2005

Citation: L. M. Kozhevnikova, “Anisotropic classes of uniqueness of the solution of the Dirichlet problem for quasi-elliptic equations”, Izv. RAN. Ser. Mat., 70:6 (2006), 93–128; Izv. Math., 70:6 (2006), 1165–1200

Citation in format AMSBIB
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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. M. Kozhevnikova, “Behaviour at infinity of solutions of pseudodifferential elliptic equations in unbounded domains”, Sb. Math., 199:8 (2008), 1169–1200  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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  mathnet  zmath  elib
    3. 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  mathnet  zmath  elib
    4. 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  mathnet  zmath  elib
    5. 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  mathnet  zmath
    6. V. F. Gilimshina, F. Kh. Mukminov, “On the decay of solutions of non-uniformly elliptic equations”, Izv. Math., 75:1 (2011), 53–71  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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