Regularity Results for Nonlocal Equations by Approximation

Archive for Rational Mechanics and Analysis volume 200, pages 59–88 (2011)Cite this article

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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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.

Additional information

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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Keywords

  • Viscosity Solution
  • Elliptic Operator
  • Regularity Result
  • Nonlocal Operator
  • Nonlocal Equation