Shape derivative for a two-phase eigenvalue problem and optimal configurations in a ball
ESAIM. Proceedings, Tome 27 (2009), pp. 311-321
Cet article a éte moissonné depuis la source EDP Sciences
In this article we deal with the problem of distributing two conducting materials in a given domain, with their proportions being fixed, so as to minimize the first eigenvalue of a Dirichlet operator. When the design region is a ball, it is known that there is an optimal distribution of materials which does not involve the mixing of the materials. However, the optimal configuration even in this simple case is not known. As a step in the resolution of this problem, in this paper, we develop the shape derivative analysis for this two-phase eigenvalue problem in a general domain. We also obtain a formula for the shape derivative in the form of a boundary integral and obtain a simple expression for it in the case of a ball. We then present some numerical calculations to support our conjecture that the optimal distribution in a ball should consist in putting the material with higher conductivity in a concentric ball at the centre.
Affiliations des auteurs :
Carlos Conca 1 ; Rajesh Mahadevan 2 ; Leon Sanz 1
@article{EP_2009_27_a18,
author = {Carlos Conca and Rajesh Mahadevan and Leon Sanz},
title = {Shape derivative for a two-phase eigenvalue problem and optimal configurations in a ball},
journal = {ESAIM. Proceedings},
pages = {311--321},
year = {2009},
volume = {27},
doi = {10.1051/proc/2009034},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009034/}
}
TY - JOUR AU - Carlos Conca AU - Rajesh Mahadevan AU - Leon Sanz TI - Shape derivative for a two-phase eigenvalue problem and optimal configurations in a ball JO - ESAIM. Proceedings PY - 2009 SP - 311 EP - 321 VL - 27 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/2009034/ DO - 10.1051/proc/2009034 LA - en ID - EP_2009_27_a18 ER -
%0 Journal Article %A Carlos Conca %A Rajesh Mahadevan %A Leon Sanz %T Shape derivative for a two-phase eigenvalue problem and optimal configurations in a ball %J ESAIM. Proceedings %D 2009 %P 311-321 %V 27 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/2009034/ %R 10.1051/proc/2009034 %G en %F EP_2009_27_a18
Carlos Conca; Rajesh Mahadevan; Leon Sanz. Shape derivative for a two-phase eigenvalue problem and optimal configurations in a ball. ESAIM. Proceedings, Tome 27 (2009), pp. 311-321. doi: 10.1051/proc/2009034
Cité par Sources :