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.
Neumann to Steklov eigenvalues: Asymptotic and monotonicity results / Lamberti, PIER DOMENICO; Provenzano, Luigi. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - 147:2(2017), pp. 429-447. [10.1017/S0308210516000214]
Neumann to Steklov eigenvalues: Asymptotic and monotonicity results
LAMBERTI, PIER DOMENICO
;PROVENZANO, LUIGI
2017
Abstract
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.File | Dimensione | Formato | |
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