Proceedings of the American Mathematical Society

$W^{2,\infty}$ regularizing effect in a nonlinear, degenerate parabolic equation in one space dimension

Author(s): Espen Robstad Jakobsen
Journal: Proc. Amer. Math. Soc. 132 (2004), 3203-3213.
MSC (2000): Primary 35D10, 35B65; Secondary 35K65, 35K55, 35B37, 49L25
Posted: June 16, 2004
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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.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35D10, 35B65, 35K65, 35K55, 35B37, 49L25

Espen Robstad Jakobsen
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: erj@math.ntnu.no

DOI: 10.1090/S0002-9939-04-07577-X
PII: S 0002-9939(04)07577-X
Keywords: Degenerate parabolic equations, Hamilton-Jacobi-Bellman equations, viscosity solutions, regularizing effects, regularity
Received by editor(s): September 12, 2002
Posted: June 16, 2004
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2004, American Mathematical Society

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