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arXiv · 1310.4339

On quasilinear parabolic evolution equations in weighted Lp-spaces II

Jeremy LeCrone·Jan Pruess·Mathias Wilke
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Abstract

Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell-Stefan diffusion, and to geometric evolution equations like the surface-diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.

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Jeremy LeCrone, Jan Pruess, Mathias Wilke. 2013-10-16. On quasilinear parabolic evolution equations in weighted Lp-spaces II. https://arxiv.org/abs/1310.4339

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