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On existence of shape optimization for a p-Laplacian equation over a class of open domains

Guo Bao-Zhu., Yang D. H.

Control and Cybernetics

2014

Vol. 43, no. 1

15--31

In this paper, we introduce four new classes of open sets in general Euclidean space RN. It is shown that every such class of open sets is compact under the Hausdorff distance. The result is applied to a shape optimization problem of p-Laplacian equation. The existence of the optimal solution is presented.