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In this thesis, we apply a direct moving plane method for the equation set with singularity in B1(0). Under the conditions \( m(t)\in {C}_{loc}^{1,1}\cap {L}_{\chi } \) and \( n(t)\in {C}_{loc}^{1,1}\cap {L}_{\kappa } \) , we show the symmetry in radial direction and monotonicity of normal solutions for the equations. To obtain this result, we will use the very important narrow region principle of the equations and the key inequality.

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Symmetry of Solutions for a Fully Nonlinear Nonlocal System with Singularity

  • 会议论文

  • 发表日期：

    2025年

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  • Xiaoxue Ji

摘要

In this thesis, we apply a direct moving plane method for the equation set with singularity in B1(0). Under the conditions \( m(t)\in {C}_{loc}^{1,1}\cap {L}_{\chi } \) and \( n(t)\in {C}_{loc}^{1,1}\cap {L}_{\kappa } \) , we show the symmetry in radial direction and monotonicity of normal solutions for the equations. To obtain this result, we will use the very important narrow region principle of the equations and the key inequality.