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Ufimsk. Mat. Zh., 2014, Volume 6, Issue 2, Pages 67–77 (Mi ufa244)  

This article is cited in 1 scientific paper (total in 1 paper)

Boundedness of solutions to anisotropic second order elliptic equations in unbounded domains

L. M. Kozhevnikova, A. A. Khadzhi

Sterlitamak branch of Bashkir State University, Sterlitamak, Russia

Abstract: In the paper we study a class of anisotropic second order elliptic equations represented by the model equation
$$ \sum_{\alpha=1}^n(|u_{x_\alpha}|^{p_\alpha-2}u_{x_\alpha})_{x_\alpha}=\sum_{\alpha=1}^n(\Phi_\alpha(\mathbf x))_{x_\alpha},\quad p_n\geq\ldots\geq p_1>1. $$
We prove the boundedness of solutions to the homogeneous Dirichlet problem in unbounded domains located along one of the coordinate axes. We also establish an estimate for the solutions to the considered equations with a compactly supported right hand side that ensures a power decay of the solutions at infinity.

Keywords: Dirichlet problem, anisotropic elliptic equation, unbounded domain, boundedness of solutions, decay of solution.

Full text: PDF file (499 kB)
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English version:
Ufa Mathematical Journal, 2014, 6:2, 66–76 (PDF, 393 kB); https://doi.org/10.13108/2014-6-2-66

Document Type: Article
UDC: 517.956.25
MSC: 35J62
Received: 05.11.2013

Citation: L. M. Kozhevnikova, A. A. Khadzhi, “Boundedness of solutions to anisotropic second order elliptic equations in unbounded domains”, Ufimsk. Mat. Zh., 6:2 (2014), 67–77; Ufa Math. J., 6:2 (2014), 66–76

Citation in format AMSBIB
\Bibitem{KozKha14}
\by L.~M.~Kozhevnikova, A.~A.~Khadzhi
\paper Boundedness of solutions to anisotropic second order elliptic equations in unbounded domains
\jour Ufimsk. Mat. Zh.
\yr 2014
\vol 6
\issue 2
\pages 67--77
\mathnet{http://mi.mathnet.ru/ufa244}
\elib{http://elibrary.ru/item.asp?id=21596975}
\transl
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 2
\pages 66--76
\crossref{https://doi.org/10.13108/2014-6-2-66}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928198601}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
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