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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 672–686 (Mi smj2354)  

This article is cited in 3 scientific papers (total in 3 papers)

New a priori estimates of solutions to anisotropic elliptic equations

Ar. S. Tersenov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: Under consideration is the Dirichlet problem for singular anisotropic elliptic equations with a nonlinear source. Some new a priori estimates are obtained, implying that the solvability of the Dirichlet problem in the class of bounded solutions essentially depends on the dimension of the domain of the problem.

Keywords: anisotropic elliptic equation, Dirichlet problem.

Full text: PDF file (340 kB)
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English version:
Siberian Mathematical Journal, 2012, 53:3, 539–550

Bibliographic databases:

UDC: 517.95
Received: 13.07.2011

Citation: Ar. S. Tersenov, “New a priori estimates of solutions to anisotropic elliptic equations”, Sibirsk. Mat. Zh., 53:3 (2012), 672–686; Siberian Math. J., 53:3 (2012), 539–550

Citation in format AMSBIB
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\by Ar.~S.~Tersenov
\paper New a~priori estimates of solutions to anisotropic elliptic equations
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 3
\pages 672--686
\mathnet{http://mi.mathnet.ru/smj2354}
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\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 3
\pages 539--550
\crossref{https://doi.org/10.1134/S0037446612020346}
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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. Tersenov A.S., “on Sufficient Conditions For the Existence of Radially Symmetric Solutions of the P-Laplace Equation”, Nonlinear Anal.-Theory Methods Appl., 95 (2014), 362–373  crossref  mathscinet  zmath  isi  scopus
    2. Ar. S. Tersenov, “On the influence of gradient terms on the existence of solutions to Dirichlet problem for the $p$-Laplace equation”, J. Math. Sci., 228:4 (2018), 463–474  mathnet  crossref  crossref
    3. Ar. S. Tersenov, “Existence of radially symmetric solutions of the inhomogeneous $p$-Laplace equation”, Siberian Math. J., 57:5 (2016), 918–928  mathnet  crossref  crossref  isi  elib  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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