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 language||English (US)|
|Number of pages||29|
|Journal||Archive for Rational Mechanics and Analysis|
|State||Published - Jan 1 2014|
ASJC Scopus subject areas
- Mechanical Engineering
- Mathematics (miscellaneous)