The Study Of The Prescribed Mean Curvature Equation

In this thesis, we are concerned with the interior gradient estimate of the following k-th prescribed mean curvature equationWe generalize the results of Wang’s interior gradient estimate of this equation when f depended only on x. Under proper condition of f, we obtained the interior gradient estimate of solution by using Bernstein technique and Wang’s test function. Moreover, the Liouville property of entire solution is yielded by our interior gradiengt estimate.