A Quantitative Modulus of Continuity for the Two-Phase Stefan Problem

Paolo Baroni, Tuomo Kuusi, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We derive the quantitative modulus of continuity (Formula Presented) which we conjecture to be optimal for solutions of the p-degenerate two-phase Stefan problem. Even in the classical case p = 2, this represents a twofold improvement with respect to the early 1980’s state-of-the-art results by Caffarelli– Evans (Arch Rational Mech Anal 81(3):199–220, 1983) and DiBenedetto (Ann Mat Pura Appl 103(4):131–176, 1982), in the sense that we discard one logarithm iteration and obtain an explicit value for the exponent α(n, p).
Original languageEnglish (US)
Pages (from-to)545-573
Number of pages29
JournalArchive for Rational Mechanics and Analysis
Issue number2
StatePublished - Jan 1 2014
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Mechanical Engineering
  • Analysis
  • Mathematics (miscellaneous)


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