Dirichlet-Neumann bracketing for horn-shaped regions

M. van den Berg

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17 Citations (Scopus)


We use Dirichlet-Neumann bracketing to obtain sharp upper and lower bounds for the spectral counting function of the Dirichlet laplacian for a horn-shaped region in Rm. The first and second term (and an estimate for the remainder) in the asymptotic expansion of the spectral counting function are obtained for a region in R2 given by {(x1,x2: x1eR, x2e, ?x1?·?x2?a<1}, 2- 1 2<a<2 1 2. © 1992.

Original languageEnglish
Pages (from-to)110-120
Number of pages11
JournalJournal of Functional Analysis
Issue number1
Publication statusPublished - 15 Feb 1992


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