Analysis & PDE

  • Anal. PDE
  • Volume 8, Number 7 (2015), 1695-1706.

Asymptotics of Hadamard type for eigenvalues of the Neumann problem on $C^1$-domains for elliptic operators

Johan Thim

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This article investigates how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain in the case when the domains involved are of class C1. We consider the Laplacian and use results developed previously for the corresponding Lipschitz case. In contrast with the Lipschitz case, however, in the C1-case we derive an asymptotic formula for the eigenvalues when the domains are of class C1. Moreover, as an application we consider the case of a C1-perturbation when the reference domain is of class C1,α.

Article information

Anal. PDE, Volume 8, Number 7 (2015), 1695-1706.

Received: 18 December 2014
Accepted: 3 September 2015
First available in Project Euclid: 16 November 2017

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Zentralblatt MATH identifier

Primary: 35P05: General topics in linear spectral theory 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47A75: Eigenvalue problems [See also 47J10, 49R05] 49R05: Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49)

Hadamard formula domain variation asymptotics of eigenvalues Neumann problem $C^1$-domains


Thim, Johan. Asymptotics of Hadamard type for eigenvalues of the Neumann problem on $C^1$-domains for elliptic operators. Anal. PDE 8 (2015), no. 7, 1695--1706. doi:10.2140/apde.2015.8.1695.

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