ON SHAPE OPTIMIZATION PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN

被引：27
作者：
Dalibard, Anne-Laure [1 ]
Gerard-Varet, David [2 ,3 ]
机构：
[1] Ecole Normale Super, CNRS, DMA, F-75005 Paris, France
[2] IMJ, F-75013 Paris, France
[3] Univ Paris 07, F-75013 Paris, France
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2013年 / 19卷 / 04期
关键词：
Fractional laplacian; fhape optimization; shape derivative; moving plane method; BOUNDARY;
D O I：
10.1051/cocv/2012041
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Our concern is the computation of optimal shapes in problems involving (-Delta)(1/2). We focus on the energy J(Omega) associated to the solution u(Omega) of the basic Dirichlet problem (-Delta)(1/2) u(Omega) = 1 in Omega, u = 0 in Omega(c). We show that regular minimizers Omega of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the moving plane method.
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页码：976 / 1013
页数：38
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