The Neumann Problem of Complex Hessian Quotient Equations

被引：4

作者：

Chen, Chuanqiang ^{[1
]}

Wei, Wei ^{[2
]}

机构：

[1] Ningbo Univ, Sch Math & Stat, Ningbo 315211, Zhejiang, Peoples R China

[2] Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200433, Peoples R China

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年 / 2021卷 / 23期

关键词：

BOUNDARY-VALUE-PROBLEMS; 2ND-ORDER ELLIPTIC-EQUATIONS; MONGE-AMPERE EQUATIONS; SPECIAL LAGRANGIAN EQUATIONS; DIRICHLET PROBLEM; J-FLOW; YAMABE PROBLEM; CONVERGENCE; SINGULARITIES; MANIFOLDS;

D O I：

10.1093/imrn/rnaa081

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the Neumann problem of complex Hessian quotient equations sigma(k)(partial derivative(partial derivative) over baru)/sigma(l)(partial derivative(partial derivative) over baru) = f(z) with 0 <= l < k <= n and establish the global C-1 estimates and reduce the global 2nd derivative estimate to the estimate of double normal 2nd derivatives on the boundary. In particular, we can prove the global C-2 estimates and the existence theorem for the Neumann problem of complex Hessian quotient equations sigma(n)(partial derivative(partial derivative) over baru)/sigma(l)(partial derivative(partial derivative) over baru)= f(z) with 0 <= l < n by the method of continuity.

引用

页码：17652 / 17672

页数：21

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