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Mat. Sb. (N.S.), 1971, Volume 86(128), Number 1(9), Pages 76–89 (Mi msb3289)  

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

On the asymptotic distribution of the eigenvalues of degenerating elliptic equations of second order

V. N. Tulovskii


Abstract: Let $P$ be a differential operator of the form
$$ P=-\sum_{i,j=1}^n\frac\partial{\partial x_i}(a_{ij}(x)\varphi(x)\frac\partial{\partial x_j})+a_0(x) $$
in the domain $G\subseteq\mathbf R^n$ which has smooth boundary.
The asymptotic distribution of the eigenvalues of this operator is studied in this paper. Under certain conditions on $\varphi(x)$ and $a_{ij}(x)$, lower and upper estimates for the number of eigenvalues of $P$ are obtained.
Bibliography: 2 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 15:1, 75–87

Bibliographic databases:

UDC: 517.946+517.948.35
MSC: 35P20
Received: 06.10.1970

Citation: V. N. Tulovskii, “On the asymptotic distribution of the eigenvalues of degenerating elliptic equations of second order”, Mat. Sb. (N.S.), 86(128):1(9) (1971), 76–89; Math. USSR-Sb., 15:1 (1971), 75–87

Citation in format AMSBIB
\Bibitem{Tul71}
\by V.~N.~Tulovskii
\paper On the asymptotic distribution of the eigenvalues of degenerating elliptic equations of second order
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 86(128)
\issue 1(9)
\pages 76--89
\mathnet{http://mi.mathnet.ru/msb3289}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=301391}
\zmath{https://zbmath.org/?q=an:0231.35059}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 15
\issue 1
\pages 75--87
\crossref{https://doi.org/10.1070/SM1971v015n01ABEH001532}


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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. I. L. Vulis, M. Z. Solomyak, “Spectral asymptotics of second-order degenerate elliptic operators”, Math. USSR-Izv., 8:6 (1974), 1343–1371  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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