凸锥中的径向对称与部分超定问题
Radial symmetry and partially overdetermined problems in a convex cone
摘要：
利用适当下调和函数$P$的最大值原理和积分恒等式，得到了空间型中凸锥中部分超定边值问题解的径向对称性.在维数$2$中，我们证明了凸锥外部分超定问题的Serrin型结果。进一步，我们得到了锥上一类具有混合边界条件的本征值问题的Rellich恒等式.
英文摘要：
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.
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