Resumen de Interior regularity of conical capillary surfaces

Dirk Schwab

• 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.