论文标题
在球体上脱颖而出的椭圆方程的解决方案的凹入性
Concavity of solutions to degenerate elliptic equations on the sphere
论文作者
论文摘要
我们证明了对单位球体严格凸面域上一类简分椭圆微分方程的经典解决方案的凹入性。该证明采用合适的两点最大原理，该技术源自Korevaar，Kawohl和Kennington的作品，用于欧几里得领域的方程式。我们强调，不需要差分运算符的可不同性，而只需要一些单调性和凹陷性能。
We prove the concavity of classical solutions to a wide class of degenerate elliptic differential equations on strictly convex domains of the unit sphere. The proof employs a suitable two-point maximum principle, a technique which originates in works of Korevaar, Kawohl and Kennington for equations on Euclidean domains. We emphasize that no differentiability of the differential operator is needed, but only some monotonicity and concavity properties.
