BOUNDARY BEHAVIOR OF A NON-PARAMETRIC MINIMAL SURFACE IN ℝ3 AT A NON-CONVEX POINT
Let Ω be a domain in iR which is locally convex at each point of its boundary except one, say (0,0), Ψ be a continuous function of 9Ω, and f be the unique generalized (variational) solution of the minimal surface equation with boundary values Φ. Assume that f e C°(Ώ\{(0,0)}). Then the radial limits of f at (0,0) from all directions in Ω exist and the restriction of f to Π η Η is a classical solution to the Dirichlet problem which continuously takes on all of its boundary values, where Η is a closed half space with (0,0) e 3H. 1980 AMS Subject Classification. Primary 35J65, 35B99.