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MR2068346 35P15 (35J05 47F05)
Filonov, N. On an inequality for the eigenvalues of the Dirichlet and Neumann problems for the Laplace operator. (Russian) Algebra i Analiz 16 (2004), no. 2, 172--176; translation in St. Petersburg Math. J. 16 (2005), no. 2, 413–416
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