Global boundedness, interior gradient estimates, and boundaryregularity for the mean curvature equation with boundaryconditions

摘要

We obtain global estimates for the modulus, interior gradientestimates, and boundary H?lder continuity estimates forsolutionsuto the capillarity problem and to the Dirichletproblem for the mean curvature equation merely in terms of themean curvature, together with the boundary contact angle in thecapillarity problem and the boundary values in the Dirichletproblem.