In this paper, we obtain some important inequalities of Hessian quotient operators, and global [Formula: see text] estimates of the Neumann problem of Hessian quotient equations. By the method of continuity, we establish the existence theorem of [Formula: see text]-admissible solutions of the Neumann problem of Hessian quotient equations.
In this paper, we consider the Neumann problem of a class of mixed complex Hessian equations σ k (∂∂u) = k−1 l=0 α l (x)σ l (∂∂u) with α l positive and 2 ≤ k ≤ n, and establish the global C 1 estimates and reduce the global second derivative estimate to the estimate of double normal second derivatives on the boundary. In particular, we can prove the global C 2 estimates and the existence theorems when k = n.Mathematical Subject Classification (2010): Primary 35J60, Secondary 35B45.
Abstract. In this paper, we introduce a new auxiliary function, and establish the interior C 2 estimate for Monge-Ampère equation in dimension n = 2, which was firstly proved by Heinz [5] by a geometric method.
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