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Sven Winklmann

A Bernstein result for entire F-minimal graphs

Keywords: Bernstein result, equation of mean curvature type, anisotropic mean curvature

We consider the nonparametric Euler–Lagrange equation which arises from an elliptic parametric functional with integrand F depending on normal directions only. We show that every entire solution must be an affine linear function, if F is C³-close to the area integrand and |Du(x)|=O(|(x,u(x))|^γ), γ∈(0,1).

Analysis, Oldenbourg Wissenschaftsverlag

Print ISSN: 0174-4747
Volume: 27, 04/2007
Pages: 375 - 386

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