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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