International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 18, Pages 913-948

Global boundedness, interior gradient estimates, and boundary regularity for the mean curvature equation with boundary conditions

Fei-Tsen Liang

Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan

Received 3 July 2003

Copyright © 2004 Fei-Tsen Liang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We obtain global estimates for the modulus, interior gradient estimates, and boundary Hölder continuity estimates for solutions u to the capillarity problem and to the Dirichlet problem for the mean curvature equation merely in terms of the mean curvature, together with the boundary contact angle in the capillarity problem and the boundary values in the Dirichlet problem.