The Capillarity Problem for Compressible Liquids
  In this paper we study existence and regularity of solutions to the capillarity problem for compressible liquids in a tube. We introduce an appropriate space of functions of bounded variation, in which the energy functional recently introduced by Robert Finn can be defined. We prove existence of a locally Lipschitz minimiser in this class. 
Maria Athanassenas and Julie Clutterbuck