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A Quantitative Modulus of Continuity for the Two-Phase Stefan Problem
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 214, no 2, 545-573 p.Article in journal (Refereed) Published
Abstract [en]

We derive the quantitative modulus of continuity omega(r)=[p+ln(r0/r)](-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 alpha(n, p).

Place, publisher, year, edition, pages
2014. Vol. 214, no 2, 545-573 p.
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URN: urn:nbn:se:uu:diva-234132DOI: 10.1007/s00205-014-0762-9ISI: 000341782400006OAI: oai:DiVA.org:uu-234132DiVA: diva2:759304
Available from: 2014-10-29 Created: 2014-10-14 Last updated: 2014-10-29Bibliographically approved

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Baroni, Paolo
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