Davoli, E., Mazari, I., & Stefanelli, U. (2023). Spectral Optimization of Inhomogeneous Plates. SIAM Journal on Control and Optimization, 61(2), 852–871. https://doi.org/10.1137/21M1435203
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.
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Research Areas:
Mathematical and Algorithmic Foundations: 50% Fundamental Mathematics Research: 50%
