Volume 26, 2020
|Number of page(s)||21|
|Published online||21 September 2020|
On a two-phase Serrin-type problem and its numerical computation*
Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University,
Accepted: 5 August 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.
Mathematics Subject Classification: 35N25 / 35J15 / 35Q93 / 65K10
Key words: Two-phase / overdetermined problem / Serrin problem / shape derivative / implicit function theorem / Kohn–Vogelius functional / augmented Lagrangian
© EDP Sciences, SMAI 2020
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