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Boundary Regularity for Capillary Surfaces

Boundary Regularity for Capillary Surfaces For solutions of capillarity problems with the boundary contact angle being bounded away from 0 and π and the mean curvature being bounded from above and below, we show the Lipschitz continuity of a solution up to the boundary locally in any neighborhood in which the solution is bounded and ∂ Ω is 𝐶 2 ; the Lipschitz norm is determined completely by the upper bound of | cos θ |, together with the lower and upper bounds of 𝐻, the upper bound of the absolute value of the principal curvatures of ∂ Ω and the dimension 𝑛. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Boundary Regularity for Capillary Surfaces

Georgian Mathematical Journal , Volume 12 (2) – Jun 1, 2005

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References (13)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2005.283
Publisher site
See Article on Publisher Site

Abstract

For solutions of capillarity problems with the boundary contact angle being bounded away from 0 and π and the mean curvature being bounded from above and below, we show the Lipschitz continuity of a solution up to the boundary locally in any neighborhood in which the solution is bounded and ∂ Ω is 𝐶 2 ; the Lipschitz norm is determined completely by the upper bound of | cos θ |, together with the lower and upper bounds of 𝐻, the upper bound of the absolute value of the principal curvatures of ∂ Ω and the dimension 𝑛.

Journal

Georgian Mathematical Journalde Gruyter

Published: Jun 1, 2005

Keywords: Capillary surface; boundary regularity

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