The classical Neumann problem for a class of mixed Hessian equations

Abstract

In this paper, weestablish global 𝐶 2 estimates for a class of mixed Hessian equations with the Neumann boundary condition and obtain the existence theorem of 𝑘admissible solutions for the classical Neumann problem of these mixed Hessian equations.

The Dirichlet Problem for mixed Hessian type equations on Riemannian manifolds

“…Later the Eq. (1.3) in Neumann problem, prescribed curvature problem, complex manifolds were also discussed in [4,5,33,7,6,31,32,22].…”

The Neumann Problem of Complex Hessian Quotient Equations

“…Krylov in [19] considered the Dirichlet problem of real case of (1.1), and Guan-Zhang in [11] considered the (k − 1)-admissible solution without the sign of α k−1 and obtained the global C 2 estimates. Recently, the classical Neumann problem of real case of (1.1) is solved by the authors [4].…”