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arXiv · 1811.07156

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

Lorenzo Cavallina·Toshiaki Yachimura
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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.

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Lorenzo Cavallina, Toshiaki Yachimura. 2021-09-13. On a two-phase Serrin-type problem and its numerical computation. https://doi.org/10.1051/cocv%2F2019048

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