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

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.