Optimal $C^{1,\frac{1}{2}}$-regularity of $H$-surfaces with a free boundary

Abstract

We prove that a surface of prescribed mean curvature ($H$-surface) with free boundary on a two-dimensional $C^2$-manifold belongs to $C^{1,\frac{1}{2}}$ up to that the boundary, provided it is a-priori continuous. We allow the $H$-surface to meet the manifold non-perpendicularly and the manifold itself to have a boundary. Our result is optimal according to an example of Hildebrandt and Nitsche.

15 pages

Cited by in corpus (1)

• Projectability of stable, partially free $H$-surfaces in the non-perpendicular case