A Quantitative Modulus of Continuity for the Two-Phase Stefan Problem
Abstract
We derive the quantitative modulus of continuity 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).
- Publication:
-
Archive for Rational Mechanics and Analysis
- Pub Date:
- November 2014
- DOI:
- 10.1007/s00205-014-0762-9
- arXiv:
- arXiv:1401.2623
- Bibcode:
- 2014ArRMA.214..545B
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Primary 35B65. Secondary 35K65;
- 80A22
- E-Print:
- 23 pages