Inserted: 10 aug 2018
Last Updated: 10 aug 2018
Journal: SIAM J. Control Optim.
We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet--Neumann boundary conditions. We propose a new approach for the computation of the second order shape derivative of such functionals, yielding a general existence and representation theorem. In particular, we consider the $p$-torsional rigidity functional for $p \geq 2$.