An Lp regularity theory for harmonic maps

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Abstract

Motivated by the harmonic map heat flow, we consider maps between Riemannian manifolds such that the tension field belongs to an Lp-space. Under an appropriate smallness condition, a certain degree of regularity follows. For suitable solutions of the harmonic map heat flow, we have a partial regularity result as a consequence.

Original languageEnglish
Pages (from-to)1-30
Number of pages30
JournalTransactions of the American Mathematical Society
Volume367
Issue number1
Early online date20 May 2014
DOIs
Publication statusPublished - 1 Jan 2015

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