Nonparametric minimal surfaces in R3 whose boundaries have a jump discontinuity
Open Access
- 18 February 1987
- journal article
- research article
- Published by Wiley in International Journal of Mathematics and Mathematical Sciences
- Vol. 11 (4) , 651-656
- https://doi.org/10.1155/s0161171288000791
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.Keywords
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