Stability analysis of the two-phase torsional rigidity near a radial configuration

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1889-1900
Number of pages12
JournalApplicable Analysis
Issue number10
Publication statusPublished - 2019 Jul 27


  • 49Q10
  • Torsion problem
  • elliptic PDE
  • optimization problem
  • shape derivative
  • spherical harmonics

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Stability analysis of the two-phase torsional rigidity near a radial configuration'. Together they form a unique fingerprint.

Cite this