| σ2 Hessian方程的Pogorelov型C2 内估计及应用 |
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| 引用本文： | 缪正武.σ2 Hessian方程的Pogorelov型C2 内估计及应用[J].浙江大学学报(理学版),2019,46(6):680-685. |
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| 作者姓名： | 缪正武 |
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| 作者单位： | 浙江工业大学 理学院，浙江 杭州 310023 |
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| 基金项目： | 浙江省大学生科技创新活动计划——新苗人才计划(2017R403049). |
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| 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Γ3?=λ=(λ1,λ2,?,λn)∈Rn:σ1(λ)>0,σ2(λ|i)>0,1≤i≤n![]() ![]() 。利用σ2![]() ![]() 算子的最优凹性，给出了σ2Hessian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Γ3?-![]() ![]() 凸整解为二次多项式。
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| 关 键 词： | σ2Hessian程 最优凹性 C2内估计 |
| 收稿时间： | 2018-09-12 |
The Pogorelov interior C2 estimate of σ2 Hessian equations and its application |
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| MIAO Zhengwu.The Pogorelov interior C2 estimate of σ2 Hessian equations and its application[J].Journal of Zhejiang University(Sciences Edition),2019,46(6):680-685. |
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| Authors: | MIAO Zhengwu |
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| Institution: | College of Science, Zhejiang University of Technology, Hangzhou 310023, China |
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| Abstract: | 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 Γ3?=λ=(λ1,λ2,?,λn)∈Rn:σ1(λ)>0,σ2(λ|i)>0,1≤i≤n![]() ![]() . And further uses the optimal concave ofσ2![]() ![]() operator to give the Pogorelov interiorC2![]() ![]() estimate ofσ2![]() ![]() Hessian equations. Then, to prove that the Γ3?-![]() ![]() convex entire solution of σ2(D2u(x))=1,x∈Rn![]() ![]() is a quadratic polynomial if u![]() ![]() satisfies a quadratic growth condition. |
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| Keywords: | σ2 Hessian equations optimal concavity interior C2 estimate |
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