Bernstein-type techniques for 2D free boundary graphs

Details Bernstein-type techniques for 2D free boundary graphs Bernstein-type techniques for 2D free boundary graphs

2006-12-15

arxiv.org/abs/math/0612454v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

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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