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

Research output: Contribution to journalArticle

Abstract

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
Volume98
Issue number10
DOIs
Publication statusPublished - 2019 Jul 27

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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