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

-curvature problem for all

1 < p < k + 1 {1<p<k+1}

and all contact angles

θ ∈ ( 0 , π 2 ) {\theta\in(0,\frac{\pi}{2})}

.