JournalsaihpcVol. 39, No. 3pp. 749–760

A Bernstein-type theorem for minimal graphs over convex domains

  • Nick Edelen

    University of Notre Dame, United States of America
  • Zhehui Wang

    Chinese Academy of Sciences, Beijing, China
A Bernstein-type theorem for minimal graphs over convex domains cover
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Abstract

Given any n2n \geq 2, we show that if ΩRn\Omega \subsetneq \mathbb{R}^n is an open convex domain (e.g. a half-space), and u ⁣:ΩRu \colon \Omega \to \mathbb{R} is a solution to the minimal surface equation which agrees with a linear function on δΩ\delta \Omega, then uu must itself be linear.

Cite this article

Nick Edelen, Zhehui Wang, A Bernstein-type theorem for minimal graphs over convex domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), no. 3, pp. 749–760

DOI 10.4171/AIHPC/18