The classical Neumann problem for a class of mixed Hessian equations
Chuan-Qiang Chen, Li Chen, Ni Xiang
TL;DR
This paper develops global second-order derivative estimates and proves the existence of solutions for a class of mixed Hessian equations with Neumann boundary conditions, advancing understanding of these nonlinear PDEs.
Contribution
It provides the first comprehensive C^2 estimates and existence results for the Neumann problem of mixed Hessian equations.
Findings
Established global C^2 estimates for mixed Hessian equations.
Proved existence of k-admissible solutions under Neumann boundary conditions.
Extended classical results to a broader class of nonlinear PDEs.
Abstract
In this paper, we establish global C^2 estimates for a class of mixed Hessian equations with Neumann boundary condition, and obtain the existence theorem of k-admissible solutions for the classical Neumann problem of these mixed Hessian equations.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Geometry and complex manifolds