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.
Cite this article
Davide Buoso, Laura Mercredi Chasman, Luigi Provenzano, On the stability of some isoperimetric inequalities for the fundamental tones of free plates. J. Spectr. Theory 8 (2018), no. 3, pp. 843–869DOI 10.4171/JST/214