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Continuity of the temperature in the two-phase Stefan problem

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Abstract

The classical two-phase Stefan problem, a model for ice-water melting, gives rise to a singular, nonlinear partial differential equation which admits a unique weak solution. Here we prove that this solution, and therefore the temperature in the Stefan problem, are continuous.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis

    L. A. Caffarelli & L. C. Evans

  2. Department of Mathematics, University of Maryland, College Park

    L. A. Caffarelli & L. C. Evans

Authors
  1. L. A. Caffarelli
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  2. L. C. Evans
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Additional information

Communicated by J. Serrin

This work was supported in part by NSF Grant 7406375 A01, by NSF Grant MCS 77-01952, and by the Alfred Sloan Foundation,

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Caffarelli, L.A., Evans, L.C. Continuity of the temperature in the two-phase Stefan problem. Arch. Rational Mech. Anal. 81, 199–220 (1983). https://doi.org/10.1007/BF00250800

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  • DOI: https://doi.org/10.1007/BF00250800

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