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Spectral asymptotics of a nonself-adjoint elliptic differential operator with an indefinite weight function. (English. Russian original) Zbl 1176.35121

Differ. Equ. 45, No. 4, 549-557 (2009); translation from Differ. Uravn. 45, No. 4, 534-542 (2009).
Summary: We compute the leading term of the asymptotics of the angular eigenvalue distribution function of the problem \(Au = \lambda \omega (x)u(x)\) in a bounded domain \(\Omega \subset\mathbb R^n\), where \(A\) is an elliptic differential operator of order \(2m\) with domain \(D(A) \subset W _m^{2m} (\Omega)\). The weight function \(\omega (x) (x\in \Omega )\) is indefinite and can also take zero values on a set of positive measure.

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35P15 Estimates of eigenvalues in context of PDEs
47F05 General theory of partial differential operators
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