Existence and stability results for an isoperimetric problem with a non-local interaction of Wasserstein type
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS(2022)
摘要
The aim of this paper is to prove the existence of minimizers for a variational problem involving the minimization under volume constraint of the sum of the perimeter and a non-local energy of Wasserstein type. This extends previous partial results to the full range of parameters. We also show that in the regime where the perimeter is dominant, the energy is uniquely minimized by balls.
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关键词
Non-local isoperimetric problem, optimal transport, existence of minimizers
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