论文标题
在有限的$（Q-1）$ - 毛细血管障碍物问题中的自由边界的测量
On the finite $(Q-1)$-Hausdorff measure of the free boundary in the subelliptic obstacle problem
论文作者
论文摘要
在本说明中，我们证明了有限的$ {（q-1）} $ - hausdorff的障碍物$ \ mathbb {g} $中障碍物问题中的自由边界的测量。在这里，$ q $表示$ \ mathbb {g} $的均匀维度。我们的主要结果定理1.1构成了由于咖啡雷利引起的欧几里得结果的下层次对应物，但是由于缺乏左右不变的矢量场的换理，分析变得复杂。这种障碍是通过使用右转导数以及受到咖啡雷尔利基本作品的启发的微妙的紧凑性论证来弥补的。
In this note, we prove the finite ${(Q-1)}$-Hausdorff measure of the free boundary in the obstacle problem in a Carnot group $\mathbb{G}$. Here, $Q$ represents the homogeneous dimension of $\mathbb{G}$. Our main result, Theorem 1.1, constitutes the subelliptic counterpart of the Euclidean result due to Caffarelli, but the analysis is complicated by the lack of commutation of the left-invariant vector fields. This obstruction is compensated by the use of right-invariant derivatives, and by a delicate compactness argument inspired to Caffarelli's fundamental works.
