We will discuss existence and regularity results for energy minimising compressible liquids in capillary tubes. This is a new area of research, the model having been introduced only recently by R. Finn.
In order to establish existence we introduce a class of functions of bounded variation, for which we can define the energy in a measure theoretical manner. We obtain height estimates after proving an extension of Stampacchia's Lemma, needed in our case. Existence then follows via a compactness result.
Some cute analytic tricks give us Lipschitz continuity of minimisers, so that full regularity can follow by a recent result by Athanassenas and Finn for the stationary case.
This is joint work with Maria Athanassenas.
 
 
 
 

Convenor: Maria Athanassenas