A curvature estimate for open surfaces subject to a general mean curvature operator and natural contact conditions at their boundary

Abstract

In the seventies, L. Simon showed that the main curvatures of two-dimensional hypersurfaces obeying a general equation of mean curvature type are a priori bounded by the Hölder norm of the coefficients of the surface differential operator. This was an essentially interior estimate. In this paper, we provide a complement to the theory, proving a global curvature estimate for open surfaces that satisfy natural contact conditions at the intersection with a given boundary.