TY - JOUR
T1 - On a two-phase Serrin-type problem and its numerical computation
AU - Cavallina, Lorenzo
AU - Yachimura, Toshiaki
N1 - Funding Information:
∗This research was partially supported by the Challenging Exploratory Research No.16K13768 of Japan Promotion of Science and the Grant-in-Aid for JSPS Fellows No. 18J11430 and No. 19J12344.
Publisher Copyright:
© 2020 EDP Sciences, SMAI.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Augmented Lagrangian
KW - Implicit function theorem
KW - Kohn-Vogelius functional
KW - Overdetermined problem
KW - Serrin problem
KW - Shape derivative
KW - Two-phase
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U2 - 10.1051/cocv/2019048
DO - 10.1051/cocv/2019048
M3 - Article
AN - SCOPUS:85091994995
SN - 1292-8119
VL - 26
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
M1 - 65
ER -