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On a two-phase Serrin-type problem and its numerical computation (1811.07156v2)
Published 17 Nov 2018 in math.AP
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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