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On convex sets that minimize the average distance

Antoine Lemenant;  Edoardo Mainini — 2012

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the compact and convex sets K ⊆ Ω ⊆ ℝ2that minimize ∫ Ω ( , K ) d + λ 1 Vol ( K ) + λ 2 Per ( K ) ∫ 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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