Oblique boundary value problems for augmented Hessian equations I
Abstract
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.
Cite
@article{arxiv.1511.08935,
title = {Oblique boundary value problems for augmented Hessian equations I},
author = {Feida Jiang and Neil S. Trudinger},
journal= {arXiv preprint arXiv:1511.08935},
year = {2017}
}
Comments
Revised version containing minor clarifications