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Mat. Sb., 2006, Volume 197, Number 2, Pages 17–34 (Mi msb1508)  

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

Quasi-Weyl asymptotics of the spectrum in the Dirichlet problem

A. S. Andreev

Popov Higher Naval Academy of Radio Electronics

Abstract: A spectral problem of Dirichlet type
\begin{gather*} \sum_\alpha D^\alpha a_\alpha D^\alpha u=\mu^{-1}pu,
a_\alpha(x)\geqslant c_0>0, \qquad p(x)\in\mathbb R, \qquad x\in\Omega\subset\mathbb R^m, \end{gather*}
where $\Omega$ is a bounded set, is considered. All the natural generalizations of the classical Weyl's spectral asymptotic formula are described. The main property of these generalizations is as follows: the leading term of the asymptotic formula is an additive function of the set $\Omega$.
Bibliography: 6 titles.

DOI: https://doi.org/10.4213/sm1508

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English version:
Sbornik: Mathematics, 2006, 197:2, 153–171

Bibliographic databases:

UDC: 513.88
MSC: 35P20
Received: 19.02.2004 and 18.02.2005

Citation: A. S. Andreev, “Quasi-Weyl asymptotics of the spectrum in the Dirichlet problem”, Mat. Sb., 197:2 (2006), 17–34; Sb. Math., 197:2 (2006), 153–171

Citation in format AMSBIB
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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. A. S. Andreev, “Quasi-Weyl Asymptotics of the Spectrum of the Vector Dirichlet Problem”, Funct. Anal. Appl., 42:2 (2008), 141–143  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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