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Riesz Potentials and Nonlinear Parabolic Equations

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Abstract

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear case.

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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 e Informatica, 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 Giuseppe Mingione.

Additional information

Communicated by V. Šverák

To Neil Trudinger for his 70th birthday

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Kuusi, T., Mingione, G. Riesz Potentials and Nonlinear Parabolic Equations. Arch Rational Mech Anal 212, 727–780 (2014). https://doi.org/10.1007/s00205-013-0695-8

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  • DOI: https://doi.org/10.1007/s00205-013-0695-8

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