Oblique boundary value problems for augmented Hessian equations II

In this paper, we continue our investigations into the global theory of oblique boundary value problems for augmented Hessian equations. We construct a global barrier function in terms of an admissible function in a uniform way when the matrix function in the augmented Hessian is only assumed regular. This enables us to derive global second derivative estimates in terms of boundary estimates which are then obtained by strengthening the concavity or monotonicity conditions in our previous work on the strictly regular case. Finally we give some applications to existence theorems which embrace standard Hessian equations as special cases.Research supported by National Natural Science Foundation of China (No. 11401306), Australian Research Council (No. DP1094303), China Postdoctoral Science Foundation (No. 2015M571010) and Jiangsu Natural Science Foundation of China (No. BK20140126)