A product estimate, the parabolic Weyl lemma and applications

Joa Weber

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arXiv · 0910.2739

A product estimate, the parabolic Weyl lemma and applications

Joa Weber

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Abstract

We prove a product estimate that allows to estimate the quadratic first order nonlinearity of the harmonic map flow in the $L^p$ norm. Then the parabolic analogue of Weyl's lemma for the Lapace operator is established. Both results are applied to prove regularity for the heat flow by parabolic bootstrapping.

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Joa Weber. 2009-10-14. A product estimate, the parabolic Weyl lemma and applications. https://arxiv.org/abs/0910.2739

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