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Zeitschrift für Analysis und ihre Anwendungen

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Volume 15, Issue 4, 1996, pp. 819–850
DOI: 10.4171/ZAA/732

Published online: 1996-12-31

Behavior of a Bounded Non-Parametric $H$-Surface Near a Reentrant Corner

K.E. Lancaster[1] and D. Siegel[2]

(1) Wichita State University, USA
(2) University of Waterloo, Canada

We investigate the manner in which a non-parametric surface $z = f(x,y)$ of prescribed mean curvature approaches its radial limits at a reentrant corner. We find, for example, that the solution $f(x, y)$ approaches a fixed value (an extreme value of its radial limits at the corner) as a Hölder continuous function with exponent $\frac{2}{3}$ as $(x,y)$ approaches the reentrant corner non-tangentially from inside a distinguished half-space. We also mention an application of our results to a problem in the production of capacitors involving "dip-coating."

Keywords: Minimal surfaces, $H$-surfaces, reentrant corners, dip-coating

Lancaster K.E., Siegel D.: Behavior of a Bounded Non-Parametric $H$-Surface Near a Reentrant Corner. Z. Anal. Anwend. 15 (1996), 819-850. doi: 10.4171/ZAA/732