Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/44398
Title: A Quantitative Modulus of Continuity for the Two-Phase Stefan Problem
Authors: Baroni, Paolo 
Kuusi, Tuomo 
Urbano, José Miguel 
Issue Date: 2014
Publisher: Springer
Project: PEst-C/MAT/UI0324/2011 
Serial title, monograph or event: Archive for Rational Mechanics and Analysis
Volume: 214
Issue: 2
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 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).
URI: http://hdl.handle.net/10316/44398
Other Identifiers: 10.1007/s00205-014-0762-9
DOI: 10.1007/s00205-014-0762-9
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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