On a two-phase Serrin-type problem and its numerical computation
Lorenzo Cavallina, Toshiaki Yachimura · ESAIM Control Optimisation and Calculus of Variations · 2019
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.