A few shape optimization results for a biharmonic Steklov problem
Luigi Provenzano, Davide Buoso · IRIS Research product catalog (Sapienza University of Rome) · 2015
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.