Vol. 37, No. 1, 1971

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The regularity of minimal surfaces defined over slit domains

David Samuel Kinderlehrer

Vol. 37 (1971), No. 1, 109–117
Abstract

Let Ω denote the disc x12 + x22 < r2 in the x = (x1,x2) plane from which the segment {0 x1 < r,x2 = 0} has been deleted. Suppose that u(x) C0(Ω) is a solution to the minimal surface equation in Ω ((1) below) and attains boundary values f(x1) C1(0 < α < 1) on the slit {0 x1 < r,x2 = 0}. We shall prove here that the gradient of u,Du = (ux1,ux2), is continuous at the origin x = 0.

Mathematical Subject Classification 2000
Primary: 53A10
Milestones
Received: 26 February 1970
Published: 1 April 1971
Authors
David Samuel Kinderlehrer