A Hölder estimate for entire solutions to the two-valued minimal surface equation

Rosales, Leobardo

doi:10.1090/proc/12774

A Hölder estimate for entire solutions to the two-valued minimal surface equation
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by Leobardo Rosales

Proc. Amer. Math. Soc. 144 (2016), 1209-1221

DOI: https://doi.org/10.1090/proc/12774

Published electronically: November 20, 2015

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Abstract:

We prove a Hölder estimate near infinity for solutions to the two-valued minimal surface equation over $\mathbb {R}^{2} \setminus \{0\},$ and give a Bernstein-type theorem in case the solution can be extended continuously across the origin. The main results follow by modifying methods used to study exterior solutions to equations of minimal surface type.

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