Article ID Journal Published Year Pages File Type
4609496 Journal of Differential Equations 2015 41 Pages PDF
Abstract

We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding eigenvalues and prove that balls are critical domains under volume constraint. Finally, we prove an isoperimetric inequality for the first positive eigenvalue.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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