Calculus of Variations and Geometric Measure Theory
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A. Cesaroni - M. Novaga

Nonlocal minimal clusters in the plane

created by novaga on 08 Oct 2019
modified on 09 Oct 2019


Submitted Paper

Inserted: 8 oct 2019
Last Updated: 9 oct 2019

Year: 2019

ArXiv: 1910.03429 PDF


We show existence of nonlocal minimal cluster with Dirichlet boundary data. In two dimensions we show that, if the fractional parameter $s$ is sufficiently close to $1$, the only singular minimal cone consists of three half-lines meeting at $120$ degrees at a common end-point. In the case of fractional perimeter with weights, we show that there exists a unique minimal cone with three phases.


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