Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T22:34:45.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Neumann to Steklov eigenvalues: asymptotic and monotonicity results

Part of: Elliptic equations and systems Representations of solutions Partial differential equations Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  16 January 2017

Pier Domenico Lamberti  and
Luigi Provenzano
Pier Domenico Lamberti
Affiliation:
Dipartimento di Matematica ‘Tullio Levi-Civita’, Università degli Studi di Padova, Via Trieste 63, 35126 Padova, Italy ([email protected]; [email protected])
Luigi Provenzano
Affiliation:
Dipartimento di Matematica ‘Tullio Levi-Civita’, Università degli Studi di Padova, Via Trieste 63, 35126 Padova, Italy ([email protected]; [email protected])
Get access Rights & Permissions [Opens in a new window]

Extract

We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of mass concentration at the boundary of a ball. We discuss the asymptotic behaviour of the Neumann eigenvalues and find explicit formulae for their derivatives in the limiting problem. We deduce that the Neumann eigenvalues have a monotone behaviour in the limit and that Steklov eigenvalues locally minimize the Neumann eigenvalues.

Keywords

Steklov boundary conditionseigenvaluesdensity perturbationmonotonicityBessel functions

MSC classification

Secondary: 35C20: Asymptotic expansions 35P15: Estimation of eigenvalues, upper and lower bounds 35B25: Singular perturbations 35J25: Boundary value problems for second-order elliptic equations 33C10: Bessel and Airy functions, cylinder functions, $_0F_1$
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 2 , April 2017 , pp. 429 - 447
Copyright
Copyright © Royal Society of Edinburgh 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)