Capillary $L_p$-curvature problem

TL;DR

This paper establishes gradient estimates for capillary curvature equations and proves the existence of smooth, convex solutions to the capillary $L_p$-curvature problem in the half-space for specific parameters.

Contribution

It provides the first gradient estimates for a class of capillary curvature equations and demonstrates the existence of solutions for a broad range of parameters.

Findings

Gradient estimate for capillary curvature equations in half-space

Existence of smooth, convex solutions for all $1<p<k+1$ and contact angles in $(0, rac{ ext{pi}}{2})$

Solution regularity and convexity properties established

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 $L_p$-curvature problem for all $1<p<k+1$ and all contact angles $\theta\in(0,\pi/2)$.