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Improved regularity for the parabolic normalized p-Laplace equation

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Abstract

We derive regularity estimates for viscosity solutions to the parabolic normalized p-Laplace. By using approximation methods and scaling arguments for the normalized p-parabolic operator, we show that the gradient of bounded viscosity solutions is locally asymptotically Lipschitz continuous when p is sufficiently close to 2. In addition, we establish regularity estimates in Sobolev spaces.

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Acknowledgements

PA was supported by CAPES-INCTMat-Brazil. MS was supported by FAPESP grant 2021/04524-0. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brazil (CAPES)-Finance Code 001.

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Centro, São Carlos, SP, 13566-590, Brazil

    Pêdra D. S. Andrade & Makson S. Santos

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  1. Pêdra D. S. Andrade
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  2. Makson S. Santos
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Correspondence to Pêdra D. S. Andrade.

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Communicated by F.-H. Lin.

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Andrade, P.D.S., Santos, M.S. Improved regularity for the parabolic normalized p-Laplace equation. Calc. Var. 61, 196 (2022). https://doi.org/10.1007/s00526-022-02291-8

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