D. Khavinson

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One of the most celebrated problems in geometry and calculus of variations is the Bernstein problem, which asserts that a C 2 minimal graph in R 3 must necessarily be an affine plane. Following an old tradition, here minimal means of vanishing mean curvature. Bernstein [Be] established this property in 1915. Almost fifty years later a new insight of Fleming(More)
In 1934 H. Malmheden [15] discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin [7] 23 years later, it still does not seem to be widely known. In this paper we return to Malmheden's theorem, give an alternative proof of the result that allows generalization to(More)
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