We investigate the manner in which a non-parametric surface of prescribed mean curvature approaches its radial limits at a reentrant corner. We find, for example, that the solution approaches a fixed value (an extreme value of its radial limits at the corner) as a Hölder continuous function with exponent as 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 -Surface Near a Reentrant Corner. Z. Anal. Anwend. 15 (1996), no. 4, pp. 819–850