Minimizing cones for fractional capillarity problems
Serena Dipierro
University of Western Australia, Crawley, AustraliaFrancesco Maggi
The University of Texas at Austin, USAEnrico Valdinoci
University of Western Australia, Crawley, Australia
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Abstract
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.
Cite this article
Serena Dipierro, Francesco Maggi, Enrico Valdinoci, Minimizing cones for fractional capillarity problems. Rev. Mat. Iberoam. 38 (2022), no. 2, pp. 635–658
DOI 10.4171/RMI/1289