Preprint 2003-010

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

Espen R. Jakobsen

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.

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Espen R. Jakobsen, <>
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<> January 29 2003.

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