| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 65 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2019048 | |
| 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,
Sendai
980-8579, Japan.
** Corresponding author: cava@ims.is.tohoku.ac.jp, yachimura@ims.is.tohoku.ac.jp
Received:
19
November
2018
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.