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.

中文翻译：

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球面上退化椭圆方程的解的凹度

我们在单位球的严格凸域上证明了一类广泛的退化椭圆微分方程的经典解的凹性。该证明采用了适当的两点最大值原理，该技术起源于 Korevaar、Kawohl 和 Kennington 的工作，用于欧几里得域上的方程。我们强调不需要微分算子的可微性，而只需要一些单调性和凹度特性。