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

2016/07/14 by Buoso, Davide, Chasman, L. Mercredi, Provenzano, Luigi · 1 citation
#35J30 (Primary) #35P15 #49R50 #74K20 (Secondary) #FOS: Mathematics #Optimization and Control (math.OC) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1607.04163

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.

Cited by

• Biharmonic Steklov problems with Neumann boundary conditions and spectral inequalities on differential forms

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