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Zeitschrift für Analysis und ihre Anwendungen

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Volume 4, Issue 5, 1985, pp. 429–436
DOI: 10.4171/ZAA/164

Published online: 1985-10-31

On Capillary Free Surfaces without Gravity

Erich Miersemann[1]

(1) Universität Leipzig, Germany

The non-parametric capillary problem in the absence of gravity can be replaced by a Dirichlet problem for a quasilmnear equation of mixed type by introducing a stream function. We prove a maximum principle for an expression depending on the gradient of the stream function and, furthermore, regularity properties of $C^1(\bar {\Omega}$-solutions in domains $\Omega$ with corners.

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Miersemann Erich: On Capillary Free Surfaces without Gravity. Z. Anal. Anwend. 4 (1985), 429-436. doi: 10.4171/ZAA/164