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.
Mots-clés : Two-phase, overdetermined problem, Serrin problem, shape derivative, implicit function theorem, Kohn–Vogelius functional, augmented Lagrangian
@article{COCV_2020__26_1_A65_0,
author = {Cavallina, Lorenzo and Yachimura, Toshiaki},
title = {On a two-phase {Serrin-type} problem and its numerical computation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019048},
mrnumber = {4151427},
zbl = {1450.35189},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019048/}
}
TY - JOUR AU - Cavallina, Lorenzo AU - Yachimura, Toshiaki TI - On a two-phase Serrin-type problem and its numerical computation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019048/ DO - 10.1051/cocv/2019048 LA - en ID - COCV_2020__26_1_A65_0 ER -
%0 Journal Article %A Cavallina, Lorenzo %A Yachimura, Toshiaki %T On a two-phase Serrin-type problem and its numerical computation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019048/ %R 10.1051/cocv/2019048 %G en %F COCV_2020__26_1_A65_0
Cavallina, Lorenzo; Yachimura, Toshiaki. On a two-phase Serrin-type problem and its numerical computation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 65. doi : 10.1051/cocv/2019048. http://www.numdam.org/articles/10.1051/cocv/2019048/
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Cité par Sources :
This research was partially supported by the Challenging Exploratory Research No.16K13768 of Japan Society for the Promotion of Science and the Grant-in-Aid for JSPS Fellows No. 18J11430 and No. 19J12344.
