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Optimal Lipschitz extensions and the infinity laplacian

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Abstract.

We reconsider in this paper boundary value problems for “infinity Laplacian” PDE and the relationships with optimal Lipschitz extensions of the boundary data. fairly elegant new proofs, which clarify and simplify previous work, and may be characterized by a comparison principle with appropriate cones. We in comparison with cones directly implies the variational principle associated Liouville theorem for subsolutions bounded above by planes.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, CA 93106, USA , , , , , , US

    M.G. Crandall

  2. Department of Mathematics, University of California, Berkeley, CA 94720, USA , , , , , , US

    L.C. Evans

  3. Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA , , , , , , US

    R.F. Gariepy

Authors
  1. M.G. Crandall
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  2. L.C. Evans
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  3. R.F. Gariepy
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Received: 29 May 2000 / Accepted: 12 June 2000 / Published online: 23 April 2001

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Crandall, M., Evans, L. & Gariepy, R. Optimal Lipschitz extensions and the infinity laplacian. Calc Var 13, 123–139 (2001). https://doi.org/10.1007/s005260000065

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  • DOI: https://doi.org/10.1007/s005260000065

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