This article is devoted to the study of spectral optimization for inhomogeneous plates. In particular, we consider the optimization of the first eigenvalue of a vibrating plate with respect to its thickness and/or density. We prove the existence of an optimal thickness, using fine tools hinging on topological properties of rearrangement classes. In the case of a circular plate, we provide a characterization of this optimal thickness by means of Talenti inequalities. Moreover, we prove a stability result when assuming that the thickness and the density of the plate are linearly related. This proof relies on H-convergence tools applied to the biharmonic operator.

Spectral optimization of inhomogeneous plates

U Stefanelli
2023

Abstract

This article is devoted to the study of spectral optimization for inhomogeneous plates. In particular, we consider the optimization of the first eigenvalue of a vibrating plate with respect to its thickness and/or density. We prove the existence of an optimal thickness, using fine tools hinging on topological properties of rearrangement classes. In the case of a circular plate, we provide a characterization of this optimal thickness by means of Talenti inequalities. Moreover, we prove a stability result when assuming that the thickness and the density of the plate are linearly related. This proof relies on H-convergence tools applied to the biharmonic operator.
2023
Istituto di Matematica Applicata e Tecnologie Informatiche - IMATI -
spectral optimization
two-phase problems
inhomogeneous plates
H-convergence
rearrangement inequalities
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/460666
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