## 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

#### Abstract

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

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

Dates
Accepted: 3 September 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.apde/1510843168

Digital Object Identifier
doi:10.2140/apde.2015.8.1695

Mathematical Reviews number (MathSciNet)
MR3399135

Zentralblatt MATH identifier
1336.35262

#### Citation

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. https://projecteuclid.org/euclid.apde/1510843168

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