A product estimate, the parabolic Weyl lemma and applications

Details A product estimate, the parabolic Weyl lemma and applications A product estimate, the parabolic Weyl lemma and applications

2009-10-14

arxiv.org/abs/0910.2739v1

Mathematics

Analysis of PDEs

27 pages

Scientific paper

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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