Nonparametric minimal surfaces in R 3 whose boundaries have a jump discontinuity

Kirk E. Lancaster

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-6

Abstract:

Let Ω be a domain in R 2 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.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:309032

DOI: 10.1155/S0161171288000791

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