$W^{2,\infty }$ regularizing effect in a nonlinear, degenerate parabolic equation in one space dimension
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Abstract:
In this paper we provide and analyze a nonlinear degenerate parabolic equation in one space dimension with the following smoothing property: If the initial data is only uniformly continuous, at positive times, the solution has bounded second derivatives (it belongs to $W^{2,\infty }$). We call this surprising phenomenon a $W^{2,\infty }$ regularizing effect. So far, such phenomena have only been observed in uniformly parabolic equations.References
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Additional Information
- Espen Robstad Jakobsen
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- Email: erj@math.ntnu.no
- Received by editor(s): September 12, 2002
- Published electronically: June 16, 2004
- Communicated by: David S. Tartakoff
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3203-3213
- MSC (2000): Primary 35D10, 35B65; Secondary 35K65, 35K55, 35B37, 49L25
- DOI: https://doi.org/10.1090/S0002-9939-04-07577-X
- MathSciNet review: 2073294