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This article is cited in 2 scientific papers (total in 2 papers)
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.
Received: 19.02.2004 and 18.02.2005
Citation:
A. S. Andreev, “Quasi-Weyl asymptotics of the spectrum in the Dirichlet problem”, Sb. Math., 197:2 (2006), 153–171
Linking options:
https://www.mathnet.ru/eng/sm1508https://doi.org/10.1070/SM2006v197n02ABEH003751 https://www.mathnet.ru/eng/sm/v197/i2/p17
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