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
We obtain global estimates for the modulus, interior gradient estimates, and boundary Hölder continuity estimates for solutions 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.
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