Abstract
We show that an infinity harmonic function, that is, a viscosity solution of the nonlinear PDE \({- \Delta_\infty u = -u_{x_i}u_{x_j}u_{x_ix_j} = 0}\), is everywhere differentiable. Our new innovation is proving the uniqueness of appropriately rescaled blow-up limits around an arbitrary point.
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Acknowledgements
Lawrence C. Evans is supported in part by NSF grants DMS-0500452 and DMS-1001724. Charles K. Smart is supported in part by NSF grant DMS-1004595.
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Communicated by L. Ambrosio.
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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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Evans, L.C., Smart, C.K. Everywhere differentiability of infinity harmonic functions. Calc. Var. 42, 289–299 (2011). https://doi.org/10.1007/s00526-010-0388-1
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DOI: https://doi.org/10.1007/s00526-010-0388-1