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New a priori estimates of solutions to anisotropic elliptic equations

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Ar. S. Tersenov

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Correspondence to Ar. S. Tersenov.

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Original Russian Text Copyright © 2012 Tersenov Ar. S.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 3, pp. 672–686, May–June, 2012.

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Tersenov, A.S. New a priori estimates of solutions to anisotropic elliptic equations. Sib Math J 53, 539–550 (2012). https://doi.org/10.1134/S0037446612020346

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  • DOI: https://doi.org/10.1134/S0037446612020346

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