The Dirichlet problem for a class of Hessian type equations

2014/12/22 by Heming Jiao, Tingting Wang, Jiao, Heming +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1412.6871

openalex publication_date 2014/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the C² estimates for an approximating problem under essentially optimal structure conditions. Based on these estimates, the existence of classical solutions is proved.

Related

• The Dirichlet Problem for mixed Hessian type equations on Riemannian manifolds
• On the Dirichlet problem for a class of augmented Hessian equations
• The Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds
• The classical Neumann problem for a class of mixed Hessian equations
• Hessian equations with elementary symmetric functions