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Article

Approximate Formulas for Eigenvalues of The Laplace Operator on a Torus Arising in Linear Problems with Oscillating Coefficients

Russian Journal of Mathematical Physics. 2012. Vol. 19. No. 3. P. 261-272.
Bruning J., Grushin V. V., Dobrokhotov S. Y.

In the paper, using relatively simple formulas derived in the abstract  perturbation  theory of selfadjoint operators, we obtain explicit asymptotic formulas for a family of elliptic operators of Laplace type that arise in linear problems with rapidly oscillating coefficients.