We consider a free boundary problem on three-dimensional cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. Combining analysis and computer-assisted proof, we show that when c is less than 4.3, the free boundary may pass through the vertex of the cone.

翻译：我们根据参数c考虑三维锥体的自由边界问题,研究允许自由边界穿过锥体顶端的情况。 结合分析与计算机辅助证据,我们证明当 c 小于4.3时,自由边界可以通过锥体顶端。