# Capillary Surfaces in Non-Cylindrical Domains

### G. Schindlmayr

Dreieich, Germany

## Abstract

This paper is concerned with the capillary problem in a class of non-cylindrical domains in $K \subset \mathbb R^{n+1}$ obtained by scaling a bounded cross-section $\Omega \subset \mathbb R^n$ along the vertical axis. The capillary surfaces are described in two different ways. In the first model, they are described as the boundary of a Caccioppoli set and in a second model, after transforming $K$ to a cylinder, they are described as graphs of functions on $\Omega$. The volume of the fluid is prescribed. For both models, the energy functional is derived and declared on the appropriate function space consisting of $BV$-functions. Main results are existence and a priori bounds of minimizers, using the direct methods in the calculus of variations. For the special case of a cone over the domain $\Omega$, a criterion is given to assure that the tip is not filled with liquid. Another point of examination concerns modelling the volume restriction by means of a Lagrange multiplier.

## Cite this article

G. Schindlmayr, Capillary Surfaces in Non-Cylindrical Domains. Z. Anal. Anwend. 19 (2000), no. 3 pp. 747–762

DOI 10.4171/ZAA/978