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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, Issue 1(30), Pages 90–96 (Mi vsgtu1163)  

This article is cited in 6 scientific papers (total in 6 papers)

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

Solutions of anisotropic elliptic equations in unbounded domains

L. M. Kozhevnikova, A. A. Khadzhi

Sterlitamak Branch of Bashkir State University, Sterlitamak, 453103, Russia

Abstract: In the paper the Dirichlet problem for an anisotropic quasilinear elliptic equations of the second order is considered. The upper estimates for the generalized solution of this Dirichlet problem are received, the closeness is proved for the isotropic case.

Keywords: Dirichlet problem, anisotropic equation, quasilinear elliptic equation, generalized solution, unbounded domain, decrease of the solution, existence of solution, uniqueness of the solution, Harnack inequality, domain of rotation

DOI: https://doi.org/10.14498/vsgtu1163

Full text: PDF file (162 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.956.25
MSC: Primary 35J62; Secondary 35J25, 35J15
Original article submitted 14/XI/2012
revision submitted – 17/I/2013

Citation: L. M. Kozhevnikova, A. A. Khadzhi, “Solutions of anisotropic elliptic equations in unbounded domains”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 90–96

Citation in format AMSBIB
\Bibitem{KozKha13}
\by L.~M.~Kozhevnikova, A.~A.~Khadzhi
\paper Solutions of anisotropic elliptic equations in~unbounded domains
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 1(30)
\pages 90--96
\mathnet{http://mi.mathnet.ru/vsgtu1163}
\crossref{https://doi.org/10.14498/vsgtu1163}


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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, A. A. Khadzhi, “Boundedness of solutions to anisotropic second order elliptic equations in unbounded domains”, Ufa Math. J., 6:2 (2014), 66–76  mathnet  crossref  elib
    2. A. A. Khadzhi, “Ubyvanie reshenii anizotropnykh ellipticheskikh uravnenii s mladshimi chlenami v neogranichennykh oblastyakh”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 34:5 (2014), 78–87  elib
    3. L. M. Kozhevnikova, A. A. Khadzhi, “O resheniyakh ellipticheskikh uravnenii s nestepennymi nelineinostyami v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 44–62  mathnet  crossref  zmath  elib
    4. R. Kh. Karimov, L. M. Kozhevnikova, A. A. Khadzhi, “Behavior of solutions to elliptic equations with non-power nonlinearities in unbounded domains”, Ufa Math. J., 8:3 (2016), 95–108  mathnet  crossref  mathscinet  isi  elib
    5. L. M. Kozhevnikova, A. A. Nikitina, “Qualitative properties of solutions of elliptic equations with non-power nonlinearities in $\mathbb{R}_n$”, J. Math. Sci., 228:4 (2018), 395–408  mathnet  crossref
    6. F. Kh. Mukminov, “Existence of a renormalized solution to an anisotropic parabolic problem with variable nonlinearity exponents”, Sb. Math., 209:5 (2018), 714–738  mathnet  crossref  crossref  adsnasa  isi  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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