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On stabilization of solutions of singular elliptic equations

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Abstract

We study linear and quasi-linear elliptic equations containing the Bessel operator with respect to a selected variable (so-called special variable). The well-posedness of the nonclassical Dirichlet problem (with the additional condition of evenness with respect to the special variable) in the half-space is proved, an integral representation of the solution is constructed, and a necessary and sufficient condition of stabilization is established. The stabilization is understood as follows: the solution has a finite limit as the independent variable tends to infinity along the direction orthogonal to the boundary hyperplane.

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Authors and Affiliations

  1. Computing Center of the 4th Polyclinic of Voronezh City, Russia

    A. B. Muravnik

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  1. A. B. Muravnik
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Correspondence to A. B. Muravnik.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 169–186, 2006.

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Muravnik, A.B. On stabilization of solutions of singular elliptic equations. J Math Sci 150, 2408–2421 (2008). https://doi.org/10.1007/s10958-008-0139-4

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  • DOI: https://doi.org/10.1007/s10958-008-0139-4

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