Power Convexity of Solutions to a Special Lagrangian Equation in Dimension Two
Power Convexity of Solutions to a Special Lagrangian Equation in Dimension Two
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DOI：
10.1007/s12220-022-01186-6
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发表时间：
2023-02
期刊：
影响因子：
--
通讯作者：
Wei Zhang;Qi Zhou
中科院分区：
文献类型：
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作者：
Wei Zhang;Qi Zhou
本文证明了一类特殊的二维拉格朗日方程Dirichlet问题解的幂凸性结果。这为完全非线性椭圆型边值问题的解具有幂凸性提供了新的例子，而这种幂凸性以前只有三维2-Hessian方程才知道。微观凸性原理和变形方法是其关键。
In this paper, we prove power convexity result of solution to Dirichlet problem of special Lagrangian equation in dimension two. This provides new example of fully nonlinear elliptic boundary value problem whose solution shares power convexity property previously only knew for 2-Hessian equation in dimension three. The key ingredients consist of microscopic convexity principles and deformation methods.