International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 18, Pages 913-948
doi:10.1155/S0161171204307039
Global boundedness, interior gradient estimates, and boundary
regularity for the mean curvature equation with boundary
conditions
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.
Abstract
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.