Quasi-Weyl asymptotics of the spectrum in the Dirichlet problem

A. S. Andreev

Sbornik. Mathematics, Tome 197 (2006) no. 2, pp. 153-171

Résumé

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.