JournalszaaVol. 19 , No. 3pp. 747–762

Capillary Surfaces in Non-Cylindrical Domains

  • G. Schindlmayr

    Dreieich, Germany
Capillary Surfaces in Non-Cylindrical Domains cover
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This paper is concerned with the capillary problem in a class of non-cylindrical domains in KRn+1K \subset \mathbb R^{n+1} obtained by scaling a bounded cross-section ­ ΩRn\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 KK to a cylinder, they are described as graphs of functions on Ω\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 BVBV-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 Ω\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.

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

DOI 10.4171/ZAA/978