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]
Titolo: | Neumann to Steklov eigenvalues: Asymptotic and monotonicity results | |
Autori: | ||
Data di pubblicazione: | 2017 | |
Rivista: | ||
Citazione: | 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] | |
Handle: | http://hdl.handle.net/11573/1446698 | |
Appartiene alla tipologia: | 01a Articolo in rivista |
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