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Regularity Results for Nonlocal Equations by Approximation

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Abstract

We obtain C 1,α regularity estimates for nonlocal elliptic equations that are not necessarily translation-invariant using compactness and perturbative methods and our previous regularity results for the translation-invariant case.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, USA

    Luis Caffarelli

  2. Department of Mathematics, University of Chicago, Chicago, USA

    Luis Silvestre

Authors
  1. Luis Caffarelli
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  2. Luis Silvestre
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Correspondence to Luis Silvestre.

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Communicated by L. Ambrosio

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Caffarelli, L., Silvestre, L. Regularity Results for Nonlocal Equations by Approximation. Arch Rational Mech Anal 200, 59–88 (2011). https://doi.org/10.1007/s00205-010-0336-4

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  • DOI: https://doi.org/10.1007/s00205-010-0336-4

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