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In this paper we study the compact and convex sets K ⊆ Ω ⊆ ℝ2that minimize
∫ Ω dist ( x ,K ) d x + λ 1 Vol ( K ) + λ 2 Per ( K ) for some constantsλ
1 and λ
2, that could possibly be zero. We compute in particular the second order derivative of the functional and use it to exclude...
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