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Shape deformation for vibrating hinged plates

We consider the biharmonic operator subject to homogeneous intermediate boundary conditions of Steklov‐type. We prove an analyticity result for the dependence of the eigenvalues upon domain perturbation and compute the appropriate Hadamard‐type formulas for the shape derivatives. Finally, we prove that balls are critical domains for the symmetric functions of multiple eigenvalues subject to volume constraint. Copyright © 2013 John Wiley & Sons, Ltd.