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arXiv · 2111.14171

Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary

Ali Hyder·Antonio Segatti·Yannick Sire·Changyou Wang
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Abstract

We introduce a heat flow associated to half-harmonic maps, which have been introduced by Da Lio and Rivi\`ere. Those maps exhibit integrability by compensation in one space dimension and are related to harmonic maps with free boundary. We consider a new flow associated to these harmonic maps with free boundary which is actually motivated by a rather unusual heat flow for half-harmonic maps. We construct then weak solutions and prove their partial regularity in space and time via a Ginzburg-Landau approximation. The present paper complements the study initiated by Struwe and Chen-Lin.

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Ali Hyder, Antonio Segatti, Yannick Sire, Changyou Wang. 2021-11-28. Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary. https://arxiv.org/abs/2111.14171

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