论文标题
最小化分数毛细血管问题的锥
Minimizing cones for fractional capillarity problems
论文作者
论文摘要
我们考虑了高斯毛细血管能量的分数版本。引入了一个合适的扩展问题，以得出该分数毛细管能量的局部最小化器的边界单调公式。结果，局部最小化器的爆破极限被证明随后会融合到最小化锥体。最后，我们表明，在平面案例中，只有一种可能的分数最小化锥体，该锥由Young定律的分数版本确定。
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.
