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Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2018

A sharp Bernstein-type theorem for entire minimal graphs

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Résumé

We consider entire solutions u to the minimal surface equation in R-N, with N >= 8, and we prove the following sharp result: if N - 7 partial derivatives partial derivative u/partial derivative x(j) are bounded on one side (not necessarily the same), then u is necessarily an affine function.

Dates et versions

hal-03621411 , version 1 (28-03-2022)

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Alberto Farina. A sharp Bernstein-type theorem for entire minimal graphs. Calculus of Variations and Partial Differential Equations, 2018, 57 (5), ⟨10.1007/s00526-018-1392-0⟩. ⟨hal-03621411⟩
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