Fei-tsen Liang

Boundary Regularity for Capillary Surfaces

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 $n$.

Capillary surface, boundary regularity.

MSC 2000: 35J60, 53A10