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

  title={A Quantitative Modulus of Continuity for the Two-Phase Stefan Problem},
  author={Paolo Baroni and Tuomo Kuusi and Jos{\'e} Miguel Urbano},
  journal={Archive for Rational Mechanics and Analysis},
AbstractWe derive the quantitative modulus of continuity $$\omega(r)=\left[ p+\ln \left( \frac{r_0}{r}\right)\right]^{-\alpha (n, p)},$$ω(r)=p+lnr0r-α(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… Expand
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