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


Author: Leobardo Rosales
Journal: Proc. Amer. Math. Soc. 144 (2016), 1209-1221
MSC (2010): Primary 49Q15
DOI: https://doi.org/10.1090/proc/12774
Published electronically: November 20, 2015
MathSciNet review: 3447673
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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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Additional Information

Leobardo Rosales
Affiliation: Korea Institute for Advanced Study, Seoul, South Korea
Email: lrosales@kias.re.kr

DOI: https://doi.org/10.1090/proc/12774
Received by editor(s): August 3, 2011
Received by editor(s) in revised form: July 18, 2013, March 7, 2015, and March 10, 2015
Published electronically: November 20, 2015
Additional Notes: This work was carried out while the author was at Rice University, and put in its final form while he was at the Korea Institute for Advanced Study.
Communicated by: Tatiana Toro
Article copyright: © Copyright 2015 American Mathematical Society