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We develop an integral approach to obtain interior a priori C^1, 1 estimates for convex solutions of prescribing scalar curvature equations ₂ () = f (x) as well as the Hessian equations ₂ (D²u) = f (x). This new approach can deal with the case when f is of weaker regularity. As a result, we prove that the C^1, 1 modules of the solutions depend only on the Lipschitz modules of f (x), instead of the \|f\|₂㵮 for some k 2 in all the papers we have known up to now.
Chen et al. (Tue,) studied this question.
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