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Perturbative estimates for the one-phase Stefan problem

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Abstract

We provide perturbative estimates for the one-phase Stefan free boundary problem and obtain the regularity of flat free boundaries via a linearization technique in the spirit of the elliptic counterpart established in De Silva (IFB 13, 223–238, 2011).

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Acknowledgements

The authors would like to thank Sandro Salsa and Fausto Ferrari for fruitful conversations on the topic of this paper. N.F. wishes to thank the Department of Mathematics of Columbia University for its warm hospitality.

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Authors and Affiliations

  1. Department of Mathematics, Barnard College, Columbia University, New York, NY, 10027, USA

    D. De Silva

  2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, 49126, Bologna, Italy

    N. Forcillo

  3. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    O. Savin

Authors
  1. D. De Silva
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  2. N. Forcillo
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  3. O. Savin
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Corresponding author

Correspondence to D. De Silva.

Additional information

Communicated by Luis Caffarelli.

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N.F. is partially supported by INDAM-GNAMPA-2019 project: Proprietà di regolarità delle soluzioni viscose con applicazioni a problemi di frontiera libera, and by the project: GHAIA Horizon 2020 MCSA RISE programme grant No 777822

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De Silva, D., Forcillo, N. & Savin, O. Perturbative estimates for the one-phase Stefan problem. Calc. Var. 60, 219 (2021). https://doi.org/10.1007/s00526-021-02003-8

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  • DOI: https://doi.org/10.1007/s00526-021-02003-8

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