We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely aSteklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape deriva-tives 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.
A few shape optimization results for a biharmonic Steklov problem / Provenzano, Luigi; Buoso, Davide. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 259:5(2015), pp. 1778-1818. [10.1016/j.jde.2015.03.013]
A few shape optimization results for a biharmonic Steklov problem
Luigi Provenzano;
2015
Abstract
We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely aSteklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape deriva-tives 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.File allegati a questo prodotto
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