Oblique boundary value problems for augmented Hessian equations III

Authors

Feida Jiang, Nanjing University of Information Science and TechnologyFollow
Neil Trudinger, University of WollongongFollow

RIS ID

135175

Publication Details

Jiang, F. & Trudinger, N. S. (2019). Oblique boundary value problems for augmented Hessian equations III. Communications in Partial Differential Equations, 44 (8), 708-748.

Abstract

In bounded domains, without any geometric conditions, we study the existence and uniqueness of globally Lipschitz and interior strong C 1,1 (and classical C 2 ), solutions of general semilinear oblique boundary value problems for degenerate (and non-degenerate), augmented Hessian equations, with strictly regular associated matrix functions. By establishing local second derivative estimates at the boundary and proving viscosity comparison principles, we show that the solution is correspondingly smooth near boundary points where the appropriate uniform convexity is satisfied.

Grant Number

ARC/DP170100929