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arxiv: math/0612454 · v1 · submitted 2006-12-15 · 🧮 math.AP

Bernstein-type techniques for 2D free boundary graphs

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keywords boundaryfreea-prioribernstein-typeboundconstantdimensionselliptic
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We prove an a-priori bound for the Lipschitz constant of a smooth one-phase free boundary graph F(u) in two dimensions. The function u satisfies a fully nonlinear elliptic equation in its positive side, and the gradient of u is equal to 1 on F(u).

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