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Fractional harmonic maps into manifolds in odd dimension n > 1

Calculus of Variations and Partial Differential Equations, ISSN: 0944-2669, Vol: 48, Issue: 3-4, Page: 421-445
2013
  • 26
    Citations
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  • 6
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Metrics Details

  • Citations
    26
    • Citation Indexes
      26
  • Captures
    6

Article Description

In this paper we consider critical points of the following nonlocal energy, where, is a compact k dimensional smooth manifold without boundary and n > 1 is an odd integer. Such critical points are called n/2-harmonic maps into N. We prove that (-Δ) u∈ L (IR) for every p ≥ 1 and thus u ∈ C(IR), for every 0 < α < 1. The local Hölder continuity of n/2-harmonic maps is based on regularity results obtained in [4] for nonlocal Schrödinger systems with an antisymmetric potential and on some new 3-terms commutators estimates. © 2012 Springer-Verlag Berlin Heidelberg.

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