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Stochastic homogenization of a nonconvex Hamilton–Jacobi equation

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Abstract

We present a proof of qualitative stochastic homogenization for a nonconvex Hamilton–Jacobi equations. The new idea is to introduce a family of “sub-equations” and to control solutions of the original equation by the maximal subsolutions of the latter, which have deterministic limits by the subadditive ergodic theorem and maximality.

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Acknowledgments

The third author was partially supported by NSF CAREER Award #1151919.

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Authors and Affiliations

  1. Ceremade (UMR CNRS 7534), Université Paris-Dauphine, Paris, France

    Scott N. Armstrong

  2. Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, IL, 60637, USA

    Hung V. Tran

  3. Department of Mathematics, University of California at Irvine, California, 92697, USA

    Yifeng Yu

Authors
  1. Scott N. Armstrong
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  2. Hung V. Tran
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  3. Yifeng Yu
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Correspondence to Scott N. Armstrong.

Additional information

Communicated by F. H. Lin.

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Armstrong, S.N., Tran, H.V. & Yu, Y. Stochastic homogenization of a nonconvex Hamilton–Jacobi equation. Calc. Var. 54, 1507–1524 (2015). https://doi.org/10.1007/s00526-015-0833-2

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  • DOI: https://doi.org/10.1007/s00526-015-0833-2

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