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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

international journal of mathematics and mathematical sciences

Nonparametric minimal surfaces in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$R^3 $"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math>whose boundaries have a jump discontinuity

Nonparametric minimal surfaces inR3whose boundaries have a jump discontinuity