**Fei-tsen Liang**

## Boundary Regularity for Capillary Surfaces

**Abstract:**

For solutions of capillarity problems with the boundary contact angle being
bounded away from $0$ and $\pi$ and the mean curvature being bounded from above
and below, we show the Lipschitz continuity of a solution up to the boundary
locally in any neighborhood in which the solution is bounded and
$\partial\Omega$ is $C^2$; the Lipschitz norm is determined completely by the
upper bound of $|\cos\theta|$, together with the lower and upper bounds of $H$,
the upper bound of the absolute value of the principal curvatures of
$\partial\Omega$ and the dimension $n$.

**Keywords:**

Capillary surface, boundary regularity.

**MSC 2000:** 35J60, 53A10