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Linear Potentials in Nonlinear Potential Theory

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Abstract

Pointwise gradient bounds via Riesz potentials, such as those available for the linear Poisson equation, actually hold for general quasilinear degenerate equations of p-Laplacean type. The regularity theory of such equations completely reduces to that of the classical Poisson equation up to the C 1-level.

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Authors and Affiliations

  1. Institute of Mathematics, Aalto University, P.O. Box 11100, 00076, Aalto, Finland

    Tuomo Kuusi

  2. Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/a, 43124, Parma, Italy

    Giuseppe Mingione

Authors
  1. Tuomo Kuusi
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  2. Giuseppe Mingione
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Correspondence to Tuomo Kuusi.

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Communicated by G. Dal Maso

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Kuusi, T., Mingione, G. Linear Potentials in Nonlinear Potential Theory. Arch Rational Mech Anal 207, 215–246 (2013). https://doi.org/10.1007/s00205-012-0562-z

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  • DOI: https://doi.org/10.1007/s00205-012-0562-z

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