We provide a quantitative version of the isoperimetric inequality for the fundamental tone of a biharmonic Neumann problem. Such an inequality has been recently established by Chasman adaptingWeinberger’s argument for the corresponding second order problem. Following a scheme introduced by Brasco and Pratelli for the second order case, we prove that a similar quantitative inequality holds also for the biharmonic operator. We also prove the sharpness of both such an inequality and the corresponding one for the biharmonic Steklov problem.

On the stability of some isoperimetric inequalities for the fundamental tones of free plates / Provenzano, Luigi; Chasman, Laura M.; Buoso, Davide. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - 8:3(2018), pp. 843-869. [10.4171/JST/214]

On the stability of some isoperimetric inequalities for the fundamental tones of free plates

Luigi Provenzano;
2018

Abstract

We provide a quantitative version of the isoperimetric inequality for the fundamental tone of a biharmonic Neumann problem. Such an inequality has been recently established by Chasman adaptingWeinberger’s argument for the corresponding second order problem. Following a scheme introduced by Brasco and Pratelli for the second order case, we prove that a similar quantitative inequality holds also for the biharmonic operator. We also prove the sharpness of both such an inequality and the corresponding one for the biharmonic Steklov problem.
2018
Biharmonic operator; Eigenvalues; Neumann boundary conditions; Quantitative isoperimetric inequality; Sharpness; Steklov boundary conditions; Statistical and Nonlinear Physics; Mathematical Physics; Geometry and Topology
01 Pubblicazione su rivista::01a Articolo in rivista
On the stability of some isoperimetric inequalities for the fundamental tones of free plates / Provenzano, Luigi; Chasman, Laura M.; Buoso, Davide. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - 8:3(2018), pp. 843-869. [10.4171/JST/214]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1446690
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