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On the evolution governed by the infinity Laplacian

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Abstract

We investigate the basic properties of the degenerate and singular evolution equation which is a parabolic version of the increasingly popular infinity Laplace equation. We prove existence and uniqueness results for both Dirichlet and Cauchy problems, establish interior and boundary Lipschitz estimates and a Harnack inequality, and also provide numerous explicit solutions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O.Box 35, 40014, Finland

    Petri Juutinen

  2. Mathematisches Institut, Universität zu Köln, 50923, Köln, Germany

    Bernd Kawohl

Authors
  1. Petri Juutinen
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  2. Bernd Kawohl
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Correspondence to Bernd Kawohl.

Additional information

The first author is partially supported by the ESF program ``Global and Geometric Aspects of Nonlinear Partial Differential Equations''

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Juutinen, P., Kawohl, B. On the evolution governed by the infinity Laplacian. Math. Ann. 335, 819–851 (2006). https://doi.org/10.1007/s00208-006-0766-3

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  • DOI: https://doi.org/10.1007/s00208-006-0766-3

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