Interior regularity of conical capillary surfaces

Dirk Schwab

Vol. 229 (2007), No. 2, 499–510

DOI: 10.2140/pjm.2007.229.499

Abstract

We consider capillary problems that arise physically when the equilibrium surface of a fluid with fixed volume is situated in a cone. By using a variational approach in the space of functions of bounded variation on the sphere Sⁿ, we obtain regularity results for a certain class of relative minima of the energy functional provided the volume is large enough. This special class of relative minima can be described by radial graphs.

Keywords

capillary surface, function of bounded variation, minimal set, radial graphs, regularity, cone

Mathematical Subject Classification 2000

Primary: 49N60, 49Q20, 49J45

Milestones

Received: 5 June 2005

Accepted: 6 October 2005

Published: 1 February 2007