International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1988 / Article

Open Access

Volume 11 |Article ID 309032 | https://doi.org/10.1155/S0161171288000791

Kirk E. Lancaster, "Nonparametric minimal surfaces in R3 whose boundaries have a jump discontinuity", International Journal of Mathematics and Mathematical Sciences, vol. 11, Article ID 309032, 6 pages, 1988. https://doi.org/10.1155/S0161171288000791

Nonparametric minimal surfaces in R3 whose boundaries have a jump discontinuity

Received21 Jan 1987
Revised18 Feb 1987

Abstract

Let Ω be a domain in R2 which is locally convex at each point of its boundary except possibly one, say (0,0), ϕ be continuous on Ω/{(0,0)} with a jump discontinuity at (0,0) and f be the unique variational solution of the minimal surface equation with boundary values ϕ. Then the radial limits of f at (0,0) from all directions in Ω exist. If the radial limits all lie between the lower and upper limits of ϕ at (0,0), then the radial limits of f are weakly monotonic; if not, they are weakly increasing and then decreasing (or the reverse). Additionally, their behavior near the extreme directions is examined and a conjecture of the author's is proven.

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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