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MINIMAL GRAPHS WITH DISCONTINUOUS BOUNDARY VALUES

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  01 February 2009

ROBERT HUFF  and
JOHN MCCUAN
ROBERT HUFF*
Affiliation:
Department of Mathematical Sciences, Indiana University, South Bend, IN 46634, USA (email: rohuff@iusb.edu)
JOHN MCCUAN
Affiliation:
Department of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA (email: mccuan@math.gatech.edu)
*
✉For correspondence; e-mail: rohuff@iusb.edu
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Abstract

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We construct global solutions of the minimal surface equation over certain smooth annular domains and over the domain exterior to certain smooth simple closed curves. Each resulting minimal graph has an isolated jump discontinuity on the inner boundary component which, at least in some cases, is shown to have nonvanishing curvature.

Keywords

minimal surface equationWeierstrass representationextremal lengthboundary regularity

MSC classification

Secondary: 35J67: Boundary values of solutions to elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 1 , February 2009 , pp. 75 - 95
Copyright
Copyright © Australian Mathematical Society 2009

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