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
- 26Citations
- 6Captures
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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.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84885628199&origin=inward; http://dx.doi.org/10.1007/s00526-012-0556-6; http://link.springer.com/10.1007/s00526-012-0556-6; http://link.springer.com/content/pdf/10.1007/s00526-012-0556-6; http://link.springer.com/content/pdf/10.1007/s00526-012-0556-6.pdf; http://link.springer.com/article/10.1007/s00526-012-0556-6/fulltext.html; https://dx.doi.org/10.1007/s00526-012-0556-6; https://link.springer.com/article/10.1007/s00526-012-0556-6
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