A free boundary value problem for capillary surfaces
Claus Gerhardt · Pacific Journal of Mathematics · 1980
We consider the usual capillary variational problem with an obstacle condition given on the boundary and prove existence and regularity of the solution to this problem.0* Introduction* The equilibrium surface in a capillary tube separating liquid and gas is represented mathematically as the graph of a function u solving the variational problem (0.1) J(v): = [ (1 + \Dv\Y 2 + -( \v\ 2 + ( β v > min VveBV(Ω).