Interior regularity for fractional systems

  • Luis Caffarelli

    The University of Texas at Austin, Department of Mathematics, 2515 Speedway, Austin, TX 78751, USA
  • Gonzalo Dávila

    Universidad Técnica Federico Santa María, Departamento de Matemática, Avenida España 1680, Valparaíso, Chile
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We study the regularity of solutions of elliptic fractional systems of order 2s, , 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].

Cite this article

Luis Caffarelli, Gonzalo Dávila, Interior regularity for fractional systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 1, pp. 165–180

DOI 10.1016/J.ANIHPC.2018.04.004