JournalszaaVol. 15, No. 4pp. 819–850

Behavior of a Bounded Non-Parametric HH-Surface Near a Reentrant Corner

  • K.E. Lancaster

    Wichita State University, USA
  • D. Siegel

    University of Waterloo, Canada
Behavior of a Bounded Non-Parametric $H$-Surface Near a Reentrant Corner cover
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Abstract

We investigate the manner in which a non-parametric surface z=f(x,y)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)f(x, y) approaches a fixed value (an extreme value of its radial limits at the corner) as a Hölder continuous function with exponent 23\frac{2}{3} as (x,y)(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 HH-Surface Near a Reentrant Corner. Z. Anal. Anwend. 15 (1996), no. 4, pp. 819–850

DOI 10.4171/ZAA/732