Preprint 2003-010

$W^{2,\infty}$ Regularizing Effect in a Nonlinear, Degenerate Parabolic Equation in One Space Dimension

Abstract: In this paper we provide and analyze a non-linear {\it degenerate} parabolic equation in one space dimension with the follwing 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 phenomenons have only been observed in {\it uniformly} parabolic equations.

Paper:

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Author(s):

Espen R. Jakobsen, <erj@math.ntnu.no>

Publishing information:

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Submitted by:

<erj@math.ntnu.no> January 29 2003.