Geodesic
Interior regularity for fractional systems
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 165-180.

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We study the regularity of solutions of elliptic fractional systems of order 2s, s∈(0,1), where the right hand side f depends on a nonlocal gradient and has the same scaling properties as the nonlocal operator. Under some structural conditions on the system we prove interior Hölder estimates in the spirit of [1]. Our results are stable in s allowing us to recover the classic results for elliptic systems due to S. Hildebrandt and K. Widman [11] and M. Wiegner [19].

DOI : 10.1016/j.anihpc.2018.04.004
Keywords: A priori estimates, Nonlocal semilinear systems, Fractional harmonic maps 
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Caffarelli, Luis; Dávila, Gonzalo. Interior regularity for fractional systems. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 165-180. doi : 10.1016/j.anihpc.2018.04.004. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.04.004/

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