Dirichlet-Neumann bracketing for horn-shaped regions

M. van den Berg

Dirichlet-Neumann bracketing for horn-shaped regions

M. van den Berg

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

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 R^m. 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 language	English
Pages (from-to)	110-120
Number of pages	11
Journal	Journal of Functional Analysis
Volume	104
Issue number	1
Publication status	Published - 15 Feb 1992

Cite this

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title = "Dirichlet-Neumann bracketing for horn-shaped regions",

abstract = "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 1 2. {\textcopyright} 1992.",

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N2 - 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 1 2. © 1992.

AB - 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 1 2. © 1992.

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EP - 120

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

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Dirichlet-Neumann bracketing for horn-shaped regions

Abstract

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