Gradient estimates of mean curvature equations with Neumann boundary value problems
In this paper, the authors use the techniques developed by Spruck, Lieberman, Wang and Jin-Li-Li 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 a question raised by \textit{G. M. Lieberman} [Oblique derivative problems for elliptic equations. Hackensack, NJ: World Scientific (2013; Zbl 1273.35006)]. As a consequence, the authors obtain the corresponding existence theorem for a class of mean curvature equations.
scientific article