An 𝐿^{𝑝} regularity theory for harmonic maps

Moser, Roger

doi:10.1090/S0002-9947-2014-06282-X

An $L^p$ regularity theory for harmonic maps
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Trans. Amer. Math. Soc. 367 (2015), 1-30 Request permission

Abstract:

Motivated by the harmonic map heat flow, we consider maps between Riemannian manifolds such that the tension field belongs to an $L^p$-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.

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