论文标题
凸锥中的径向对称性和部分过度确定的问题
Radial symmetry and partially overdetermined problems in a convex cone
论文作者
论文摘要
我们通过将最大原理用于合适的亚谐波函数$ p $和积分身份，从而在凸锥中以凸锥中部分过度确定的边界值问题获得径向对称性。在尺寸$ 2 $中，我们证明了在凸锥外部分过度确定问题的锯齿蛋白型结果。此外，我们获得了与锥体中混合边界条件的特征值问题的Rellich身份。
We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function $P$ and integral identities. In dimension $2$, we prove Serrin-type results for partially overdetermined problems outside a convex cone. Furthermore, we obtain a Rellich identity for an eigenvalue problem with mixed boundary conditions in a cone.
