We prove a gradient bound for solutions of a large class of oblique derivative problems using the maximum principle. Although many of the results in this work are already known, the advantage to the current approach is that it covers a larger variety of problems than previously considered by any single method. In particular, we can study the capillary equation and the false mean curvature equation with a wide range of boundary conditions.
"Gradient estimates for elliptic oblique derivative problems via the maximum principle." Adv. Differential Equations 25 (11/12) 709 - 754, November/December 2020.