Shape Optimization of an Elliptic Equation in an Exterior Domain
Gengsheng Wang, Lijuan Wang, Donghui Yang · SIAM Journal on Control and Optimization · 2006
This work concerns the shape optimization problem governed by some elliptic equations in exterior domains. The existence of optimal solutions is obtained and the so-called $\stackrel{\wedge}{\Gamma}$-property for a family ${\cal O}$ of open subsets is established; i.e., if $\Omega_m, \Omega\in {\cal O}$ are such that $\Omega_m\ra \Omega$ in the Hausdorff metric, then for any $K\subset\subset R^N\setminus \o \Omega$, there exists $m(K)>0$ such that for all $m\geq m(K), K\subset\subset R^N\setminus \o \Omega_m$.