Summary
We find a lower bound for the ratio between the first eigenvalue of any homogeneous thin plate G, which is clamped on its boundary, and the first eigenvalue of the spherical clamped plate having the same measure as G. In two dimensions, our bound is about 0.98.
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Talenti, G. On the first eigenvalue of the clamped plate. Annali di Matematica pura ed applicata 129, 265–280 (1981). https://doi.org/10.1007/BF01762146
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DOI: https://doi.org/10.1007/BF01762146