2015/11/28 by Feida Jiang, Jiang, Feida, Neil S. Trudinger +1
Mathematics · #35J66 (Primary) 35J25 #35J96 (Secondary) #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.1511.08935
openalex publication_date 2015/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study global regularity for oblique boundary value problems of augmented Hessian equations for a class of general operators. By assuming a natural convexity condition of the domain together with appropriate convexity conditions on the matrix function in the augmented Hessian, we develop a global theory for classical elliptic solutions by establishing global a priori derivative estimates up to second order. Besides the known applications for Monge-Amp`ere type operators in optimal transportation and geometric optics, the general theory here embraces prescribed mean curvature problems in conformal geometry as well as oblique boundary value problems for augmented k-Hessian, Hessian quotient equations and certain degenerate equations.