On a two-phase Serrin-type problem and its numerical computation

Lorenzo Cavallina, Toshiaki Yachimura

Research output: Contribution to journalArticlepeer-review

Abstract

We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique solvability near radially symmetric configurations by means of a perturbation argument relying on shape derivatives and the implicit function theorem. This problem is also treated numerically, by means of a steepest descent algorithm based on a Kohn-Vogelius functional.

Original languageEnglish
Article number65
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume26
DOIs
Publication statusPublished - 2020

Keywords

  • Augmented Lagrangian
  • Implicit function theorem
  • Kohn-Vogelius functional
  • Overdetermined problem
  • Serrin problem
  • Shape derivative
  • Two-phase

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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