Power Convexity of Solutions to a Special Lagrangian Equation in Dimension Two

被引：1
作者：
Zhang, Wei [1 ]
Zhou, Qi [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou, Gansu, Peoples R China
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Power convexity; Special Lagrangian equation; Constant rank theorem; CONSTANT RANK THEOREM; LEVEL SETS; ELLIPTIC PROBLEMS; DIRICHLET PROBLEM; BRUNN-MINKOWSKI; CONCAVITY; INEQUALITIES; EXISTENCE; DOMAINS; PHASES;
D O I：
10.1007/s12220-022-01186-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：13
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