Archive for Rational Mechanics and Analysis

, Volume 214, Issue 2, pp 545–573 | Cite as

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

  • Paolo Baroni
  • Tuomo Kuusi
  • José Miguel Urbano


We derive the quantitative modulus of continuity
$$\omega(r)=\left[ p+\ln \left( \frac{r_0}{r}\right)\right]^{-\alpha (n, p)},$$
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).


Weak Solution Stefan Problem Degenerate Parabolic Equation Rebalance Local Weak Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Paolo Baroni
    • 1
  • Tuomo Kuusi
    • 2
  • José Miguel Urbano
    • 3
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden
  2. 2.Institute of MathematicsAalto UniversityAaltoFinland
  3. 3.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal

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