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In this paper,we use the maximum principle to get the gradient estimate for the solutions of the prescribed mean curvature equation with Neumann boundary value problem,which gives a positive answer for the question raised by Lieberman.As a consequence,we obtain the corresponding existence theorem for a class of mean curvature equations.We also study the Hessian equation with Neumann boundary value problem.This is a joint works with Jinju Xu and Guohuan Qiu.