SIAM Journal on Control and Optimization, Vol.50, No.1, 222-242, 2012
SOME COMPACT CLASSES OF OPEN SETS UNDER HAUSDORFF DISTANCE AND APPLICATION TO SHAPE OPTIMIZATION
In this paper, we introduce three new classes of open sets in a general Euclidean space RN. It is shown that every class of open sets is compact under the Hausdorff distance. The result is then applied to a shape optimization problem of elliptic equation. The existence of the optimal solution is presented.