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1 June 2001 All time C-regularity of the interface in degenerate diffusion: a geometric approach
P. Daskalopoulos, R. Hamilton, K. Lee
Duke Math. J. 108(2): 295-327 (1 June 2001). DOI: 10.1215/S0012-7094-01-10824-7

Abstract

We study the connection between the geometry and all time regularity of the interface in degenerated diffusion. Our model considers the porous medium equation utum, m>1, with initial data u0 nonnegative, integrable, and compactly supported. We show that if the initial pressure f0=u0m is smooth up to the interface and in addition it is root-concave and also satisfies the nondegeneracy condition |Df0|≠0 at $\partial\overline {\rm supp}$f0, then the pressure fm−1 remains C-smooth up to the interface and root-concave, for all time $0 < t < ∞$. In particular, the free boundary is C-smooth for all time.

Citation

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P. Daskalopoulos. R. Hamilton. K. Lee. "All time C-regularity of the interface in degenerate diffusion: a geometric approach." Duke Math. J. 108 (2) 295 - 327, 1 June 2001. https://doi.org/10.1215/S0012-7094-01-10824-7

Information

Published: 1 June 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1017.35052
MathSciNet: MR1833393
Digital Object Identifier: 10.1215/S0012-7094-01-10824-7

Subjects:
Primary: 35K55
Secondary: 35A30, 35B65, 53C44

Rights: Copyright © 2001 Duke University Press

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Vol.108 • No. 2 • 1 June 2001
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