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Nonexistence of some nonparametric surfaces of prescribed mean curvature

Author: Kirk E. Lancaster
Journal: Proc. Amer. Math. Soc. 96 (1986), 187-188
MSC: Primary 35J60; Secondary 49F10, 53A10
MathSciNet review: 813836
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Abstract: If $ \Omega \subset {{\mathbf{R}}^2}$ has a reentrant corner, the Dirichlet problem for the equation of prescribed mean curvature $ H$ with zero boundary value has no solution when $ H$ has constant nonzero sign.

References [Enhancements On Off] (What's this?)

  • [1] A. Elcrat and K. Lancaster, Boundary behavior of a non-parametric surface of prescribed mean curvature near a reentrant corner (to appear). MR 854090 (87h:35098)
  • [2] R. Finn, Remarks relevant to minimal surfaces, and to surfaces of prescribed mean curvature, J. Analyse Math. 14 (1965), 139-160. MR 0188909 (32:6337)
  • [3] T. Higgins, Analogic experimental methods in stress analysis as exemplified by Saint-Venant's torsion problem, Experimental Stress Analysis 2 (1945), 17-27. MR 0012570 (7:41c)
  • [4] R. Gulliver, personal communication.
  • [5] G. Williams, The Dirichlet problem for the minimal surface equation with Lipschitz continuous boundary data, Research Report CMA-R41-83, Australian National Univ., 1983. MR 1394678 (97d:58054)

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Article copyright: © Copyright 1986 American Mathematical Society

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