## P. Baroni - T. Kuusi - J. M. Urbano

# A quantitative modulus of continuity for the two-phase Stefan problem

created by baroni on 14 Jan 2014

modified on 31 Aug 2017

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BibTeX]

*Published Paper*

**Inserted:** 14 jan 2014

**Last Updated:** 31 aug 2017

**Journal:** Arch. Ration. Mech. Anal.

**Volume:** 214

**Number:** 2

**Year:** 2014

**Doi:** 10.1007/s00205-014-0762-9

**Abstract:**

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 1984 state-of-the-art result by DiBenedetto and Friedman (J. reine
angew. Math., 1984), in the sense that we discard one logarithm iteration and
obtain an explicit value for the exponent $\alpha (n,p)$.

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