The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (249 KB) | Metadata | Table of Contents | ZAA summary
Volume 19, Issue 3, 2000, pp. 747–762
DOI: 10.4171/ZAA/978

Published online: 2000-09-30

Capillary Surfaces in Non-Cylindrical Domains

G. Schindlmayr[1]

(1) Dreieich, Germany

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.

Keywords: Equilibrium capillary surfaces, BV-functions, existence, Lagrange multiplier

Schindlmayr G.: Capillary Surfaces in Non-Cylindrical Domains. Z. Anal. Anwend. 19 (2000), 747-762. doi: 10.4171/ZAA/978