Interior regularity for fractional systems

Caffarelli, Luis; Dávila, Gonzalo

Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 165-180.

We study the regularity of solutions of elliptic fractional systems of order 2s, $s\in (0,1)$, 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].

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