Interior regularity for fractional systems

Luis Caffarelli, Gonzalo Dávila

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© 2018 Elsevier Masson SAS 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].
Original languageEnglish
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Publication statusPublished - 1 Jan 2018

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