摘要
提出利用拉格朗日乘子法重新证明σ2算子的最优凹性,并定义了一个凸锥■。利用σ2算子的最优凹性,给出了σ2 Hessian方程Pogorelov型C2内估计,进而证明了σ2(D2u(x))=1, x∈Rn的满足二次多项式增长条件的■凸整解为二次多项式。
The Hessian equation is an important class of completely nonlinear partial differential equations. In this paper, the author re-proves the concaveness by using the Lagrange multiplier method and defines a convex cone ■. And further uses the optimal concave of σ2 operator to give the Pogorelov interior C2 estimate of σ2 Hessian equations. Then, to prove that the ■-convex entire solution of σ2(D2 u(x)) = 1, x ∈ Rn is a quadratic polynomial if u satisfies a quadratic growth condition.
作者
缪正武
MIAO Zhengwu(College of Science,Zhejiang University of Technology,Hangzhou 310023,China)
出处
《浙江大学学报（理学版）》
CAS
CSCD
北大核心
2019年第6期680-685,共6页
Journal of Zhejiang University（Science Edition）
基金
浙江省大学生科技创新活动计划——新苗人才计划(2017R403049)
