Let Ω0 denote the unit ball of RN (N ≥ 2) centered at the origin. We suppose that Ω0 contains a core, given by a smaller concentric ball D0, made of a (possibly) different material. We discover that, depending on the relative hardness of the two materials, this radial configuration can either be a local maximizer for the torsional rigidity functional E or a saddle shape. In this paper, we consider perturbations that simultaneously act on the boundaries ∂D0 and ∂Ω0. This gives rise to resonance effects that are not present when ∂D0 and ∂Ω0 are perturbed in isolation. A detailed analysis of the sign of the second order shape derivative of E is then made possible by employing the use of spherical harmonics.
ASJC Scopus subject areas
- Applied Mathematics