| Abstract: |
| 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 calculate a critical value $c_0$ and show that when $c \leq c_0$, the free boundary may pass through the vertex of the cone. When $c > c_0$, the free boundary does not pass through the vertex of the cone. |
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