Sobolev extension operators and Neumann eigenvalues

Vladimir Golodshtein; Valerii Pchelintsev; Alexander Ukhlov

doi:10.4171/JST/295

Sobolev extension operators and Neumann eigenvalues

Vladimir Golodshtein, Valerii Pchelintsev, Alexander Ukhlov

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of the first non-trivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem(initially proposed by J. J. Sylvester in 1857).

Original language	American English
Pages (from-to)	337-353
Number of pages	17
Journal	Journal of Spectral Theory
Volume	10
Issue number	1
DOIs	https://doi.org/10.4171/JST/295
State	Published - 1 Jan 2020

Keywords

Elliptic equations
Extension operators
Sobolev spaces

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Geometry and Topology

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10.4171/JST/295

Cite this

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abstract = "In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of the first non-trivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem(initially proposed by J. J. Sylvester in 1857).",

keywords = "Elliptic equations, Extension operators, Sobolev spaces",

author = "Vladimir Golodshtein and Valerii Pchelintsev and Alexander Ukhlov",

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AU - Golodshtein, Vladimir

AU - Pchelintsev, Valerii

AU - Ukhlov, Alexander

N1 - Publisher Copyright: © European Mathematical Society.

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Y1 - 2020/1/1

N2 - In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of the first non-trivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem(initially proposed by J. J. Sylvester in 1857).

AB - In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of the first non-trivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem(initially proposed by J. J. Sylvester in 1857).

KW - Elliptic equations

KW - Extension operators

KW - Sobolev spaces

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U2 - 10.4171/JST/295

DO - 10.4171/JST/295

M3 - Article

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VL - 10

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EP - 353

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 1

ER -

Sobolev extension operators and Neumann eigenvalues

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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