Abstract
We present a new, easy, and elementary proof of Jensen’s Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.
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Acknowledgements
The authors warmly thank Michael Crandall for his many valuable suggestions and remarks. This short article was also improved by the helpful comments of Stephanie Somersille, Kelli Talaska, and Yifeng Yu.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Armstrong, S.N., Smart, C.K. An easy proof of Jensen’s theorem on the uniqueness of infinity harmonic functions. Calc. Var. 37, 381–384 (2010). https://doi.org/10.1007/s00526-009-0267-9
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DOI: https://doi.org/10.1007/s00526-009-0267-9