International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 637615 | https://doi.org/10.1155/S0161171204307039

Fei-Tsen Liang, "Global boundedness, interior gradient estimates, and boundary regularity for the mean curvature equation with boundary conditions", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 637615, 36 pages, 2004. https://doi.org/10.1155/S0161171204307039

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

Received03 Jul 2003

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.


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