A capillarity problem for compressible liquids

Maria Athanassenas and Julie Clutterbuck

Vol. 243 (2009), No. 2, 213–232

DOI: 10.2140/pjm.2009.243.213

Abstract

We study the 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 introduced recently by Robert Finn can be defined. We prove existence of a locally Lipschitz minimizer in this class.

Keywords

capillarity, function of bounded variation, compressible liquid

Mathematical Subject Classification 2000

Primary: 49Q20, 76B45, 76N10

Milestones

Received: 2 December 2008

Accepted: 25 February 2009

Published: 1 December 2009