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 0.43, the free boundary may pass through the vertex of the cone.
翻译:我们考虑三维锥体的自由边界问题,这取决于参数C,研究自由边界何时被允许穿过锥体的顶端。 结合分析和计算机辅助证据,我们证明当 c 小于0.43时,自由边界可以通过锥体的顶端。