Capillary L p -curvature problem

Abstract We prove a gradient estimate for a class of capillary curvature equations in the half-space. As an application, we prove the existence of an even, smooth, strictly convex solution to the even capillary L p {L_{p}} -curvature problem for all 1 < p < k + 1 {1 and all contact angles θ ∈ ( 0 , π 2 ) {\theta\in(0,\frac{\pi}{2})} .