In this paper we establish some symmetry results for positive solutions of semilinear elliptic equations with mixed boundary conditions. In particular, we show that the positive solution in a super-spherical sector must be symmetric. The monotonicity property is also proved. Our proof is based on the well-known moving plane methods.

中文翻译：

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超球面混合边界条件椭圆方程正解的对称性

在本文中，我们建立了具有混合边界条件的半线性椭圆方程正解的一些对称结果。特别是，我们证明了超球形扇区中的正解必须是对称的。也证明了单调性。我们的证明基于众所周知的移动平面方法。