Minimizing fractional harmonic maps on the real line in the supercritical regime

Vincent Millot; Yannick Sire; Hui Yu

doi:10.3934/dcds.2018266

Article Contents

2018, Volume 38, Issue 12: 6195-6214. Doi: 10.3934/dcds.2018266

This issue Previous Article Principal Floquet subspaces and exponential separations of type Ⅱ with applications to random delay differential equations Next Article Some questions looking for answers in dynamical systems

Minimizing fractional harmonic maps on the real line in the supercritical regime

1.
Université Paris Diderot, Lab. J.L.Lions (CNRS UMR 7598), Paris, France
2.
Johns Hopkins University, Department of Mathematics, Baltimore, USA
3.
Columbia University, Department of Mathematics, New York, USA

Dedicated to Rafael de la Llave on the occasion of his 60th birthday with admiration and friendship

Received: September 30, 2017

Revised: March 31, 2018

Published: November 2018

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Abstract

This article addresses the regularity issue for minimizing fractional harmonic maps of order s∈(0, 1/2) from an interval into a smooth manifold. Hölder continuity away from a locally finite set is established for a general target. If the target is the standard sphere, then Hölder continuity holds everywhere.

Keywords:

Fractional harmonic maps,
supercritical variational elliptic problems,
partial regularity.

Mathematics Subject Classification: 35J70, 35S15, 35B65.

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References

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