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

### K.E. Lancaster

Wichita State University, USA### D. Siegel

University of Waterloo, Canada

## Abstract

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."

## Cite this article

K.E. Lancaster, D. Siegel, Behavior of a Bounded Non-Parametric $H$-Surface Near a Reentrant Corner. Z. Anal. Anwend. 15 (1996), no. 4, pp. 819–850

DOI 10.4171/ZAA/732