Interior C^{2} estimates for the Hessian quotient type equation.

In this paper, we study the interior C^{2} estimates for a type of Hessian quotient equation. If k<n, we establish the interior C^{2} estimates. If k=n, we construct the examples, namely, the irregular solutions to the Monge-Ampère type equations. This result can be viewed as a generalization of the results of Pogorelov [ The Minkowski multidimensional problem , V. H. Winston & Sons, Washington, 1978, page 81] or Urbas [Indiana Univ. Math. J. 1990, pp. 355-382, Theorem 2]. [ABSTRACT FROM AUTHOR]