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C 1,α regularity for infinity harmonic functions in two dimensions

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Abstract

We propose a new method for showing C 1, α regularity for solutions of the infinity Laplacian equation and provide full details of the proof in two dimensions. The proof for dimensions n ≥ 3 depends upon some conjectured local gradient estimates for solutions of certain transformed PDE.

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References

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Authors and Affiliations

  1. Department of Mathematics, UC Berkeley, Berkeley, CA, USA

    Lawrence C. Evans

  2. Department of Mathematics, Columbia University, New York, USA

    Ovidiu Savin

Authors
  1. Lawrence C. Evans
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  2. Ovidiu Savin
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Corresponding author

Correspondence to Lawrence C. Evans.

Additional information

LCE is supported in part by NSF Grant DMS-0500452. OS was supported in part by the Miller Institute for Basic Research in Science, Berkeley.

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Evans, L.C., Savin, O. C 1,α regularity for infinity harmonic functions in two dimensions. Calc. Var. 32, 325–347 (2008). https://doi.org/10.1007/s00526-007-0143-4

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  • DOI: https://doi.org/10.1007/s00526-007-0143-4

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