A variational method for second order shape derivatives

Abstract

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 grater than or equal to 2.

Submitted paper. 29 pages

References in corpus (1)

• Shape derivatives for minima of integral functionals

Cited by in corpus (2)

• On Blaschke-Santaló diagrams for the torsional rigidity and the first Dirichlet eigenvalue
• Second-order derivative of domain-dependent functionals along Nehari manifold trajectories