Calculus of Variations and Geometric Measure Theory

S. Dipierro - F. Maggi - E. Valdinoci

Minimizing cones for fractional capillarity problems

created by maggi on 17 Aug 2020
modified on 29 Aug 2020



Inserted: 17 aug 2020
Last Updated: 29 aug 2020

Year: 2020

We consider a fractional version of Gauss capillarity energy. A suitable extension problem is introduced to derive a boundary monotonicity formula for local minimizers of this fractional capillarity energy. As a consequence, blow-up limits of local minimizers are shown to subsequentially converge to minimizing cones. Finally, we show that in the planar case there is only one possible fractional minimizing cone, the one determined by the fractional version of Young's law.