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Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2021

Partial regularity for fractional harmonic maps into spheres

Marc Pegon

Résumé

This article addresses the regularity issue for stationary or minimizing fractional harmonic maps into spheres of order s ∈ (0, 1) in arbitrary dimensions. It is shown that such fractional harmonic maps are C ∞ away from a small closed singular set. The Hausdorff dimension of the singular set is also estimated in terms of s ∈ (0, 1) and the stationar-ity/minimality assumption.
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Dates et versions

hal-02297231 , version 1 (25-09-2019)
hal-02297231 , version 2 (16-01-2020)
hal-02297231 , version 3 (12-10-2020)

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Vincent Millot, Marc Pegon, Armin Schikorra. Partial regularity for fractional harmonic maps into spheres. Archive for Rational Mechanics and Analysis, 2021, 242 (2), pp.747-825. ⟨10.1007/s00205-021-01693-w⟩. ⟨hal-02297231v3⟩
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