Kirk E. Lancaster, "Nonparametric minimal surfaces in 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 whose boundaries have a jump discontinuity
Let be a domain in which is locally convex at each point of its boundary except possibly one, say , be continuous on with a jump discontinuity at and be the unique variational solution of the minimal surface equation with boundary values . Then the radial limits of at from all directions in exist. If the radial limits all lie between the lower and upper limits of at , then the radial limits of 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.
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