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A uniform gradient for functions u which satisfy a system of N second-orderpartial differential inequalities is given in this paper. Some structureconditions are given for the coefficients of the matrices of second-order termsand of first-order terms. This result can be applied to study the gradientestimate of a class of second-order degenerate elliptic partial differentialequations.

An Interior Gradient Estimate for a class of Second Order Partial Differential Inequalities