This article is cited 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.

UDC: 513.88

MSC: 35P20

Received: 19.02.2004 and 18.02.2005

DOI: 10.4213/sm1508

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

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