SIAM Journal on Control and Optimization, Vol.51, No.1, 253-272, 2013
ON CONVERGENCE OF BOUNDARY HAUSDORFF MEASURE AND APPLICATION TO A BOUNDARY SHAPE OPTIMIZATION PROBLEM
This is the second part of our recent work [SIAM J. Control Optim., 50 (2012), pp. 222-242] on new open sets class and related shape optimization. In this paper, we are concerned with a boundary shape optimization problem. It is shown that the convergence of the open sets class under the Hausdorff distance implies the convergence of the Hausdorff measure on the boundary. The existence of the boundary shape optimization is concluded.