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arXiv · 1711.11143

Regularity Properties of Degenerate Diffusion Equations with Drifts

Inwon Kim·Yuming Zhang
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Abstract

This paper considers a class of nonlinear, degenerate drift- diffusion equations. We study well-posedness and regularity properties of the solutions, with the goal to achieve uniform Hölder regularity in terms of $L^p$-bound on the drift vector field. A formal scaling argument yields that the threshold for such estimates is $p=d$, while our estimates are for $p>d+\frac{4}{d+2}$. On the other hand we are able to show by a series of examples that one needs $p>d$ for such estimates, even for divergence free drift.

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Inwon Kim, Yuming Zhang. 2017-11-29. Regularity Properties of Degenerate Diffusion Equations with Drifts. https://arxiv.org/abs/1711.11143

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