An improved modulus of continuity for the two-phase Stefan problem
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- by Naian Liao;
- Trans. Amer. Math. Soc. 377 (2024), 6023-6041
- DOI: https://doi.org/10.1090/tran/9093
- Published electronically: June 28, 2024
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Abstract:
The known logarithmic-type modulus of continuity is improved for weak solutions to the two-phase Stefan problem in low space dimensions. In the two dimensional problem, the modulus becomes $\boldsymbol \omega (r)\approx \operatorname {exp}\{-c|\operatorname {ln} r|^{\frac 12}\},$ for some $c\in (0,1)$. In the one dimensional problem, the modulus becomes Hölder-type. The main merit lies in a delicate, potential theoretical estimate that sharpens the expansion of positivity for non-negative super-solutions to parabolic equations. Our argument offers a unified approach to the state-of-the-art moduli in all dimensions.References
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Bibliographic Information
- Naian Liao
- Affiliation: Fachbereich Mathematik, Paris Lodron Universität Salzburg, Hellbrunner Str. 34, 5020 Salzburg, Austria
- MR Author ID: 980634
- Email: naian.liao@plus.ac.at
- Received by editor(s): March 25, 2021
- Published electronically: June 28, 2024
- Additional Notes: The author was supported by the FWF–Project P36272–N “On the Stefan type problems”.
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 377 (2024), 6023-6041
- MSC (2020): Primary 35K65; Secondary 35B65, 80A22
- DOI: https://doi.org/10.1090/tran/9093