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arXiv · 1607.04163

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

Davide Buoso·L. Mercredi Chasman·Luigi Provenzano
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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 adapting Weinberger'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.

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Davide Buoso, L. Mercredi Chasman, Luigi Provenzano. 2016-07-14. On the stability of some isoperimetric inequalities for the fundamental tones of free plates. https://arxiv.org/abs/1607.04163

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