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In this paper, we continue our investigations into the global theory ofoblique boundary value problems for augmented Hessian equations. We construct aglobal barrier function in terms of an admissible function in a uniform waywhen the matrix function in the augmented Hessian is only assumed regular. Thisenables us to derive global second derivative estimates in terms of boundaryestimates which are then obtained by strengthening the concavity ormonotonicity conditions in our previous work on the strictly regular case.Finally we give some applications to existence theorems which embrace standardHessian equations as special cases.

Oblique boundary value problems for augmneted Hessian equations II