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Regularity Results for Fully Nonlinear Integro-Differential Operators with Nonsymmetric Positive Kernels: Subcritical Case

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Abstract

We introduce a class of fully nonlinear integro-differential operators with possible nonsymmetric kernels. For the index σ of the operator in (1, 2) (subcritical case), we introduce a very general class of fully nonlinear integro-differential operators and obtain a comparison principle, a nonlocal version of the Alexandroff–Backelman–Pucci estimate, a Harnack inequality, a Hölder regularity, and an interior C1,α-regularity for equations associated with such a class.

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Authors and Affiliations

  1. Department of Mathematics Education, Korea University, Seoul, 136-701, Korea

    Yong-Cheol Kim

  2. Department of Mathematics, Seoul National University, Seoul, 151-747, Korea

    Ki-Ahm Lee

  3. Korea Institute for Advanced Study, Seoul, 130-722, Korea

    Ki-Ahm Lee

Authors
  1. Yong-Cheol Kim
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  2. Ki-Ahm Lee
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Correspondence to Yong-Cheol Kim.

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Kim, YC., Lee, KA. Regularity Results for Fully Nonlinear Integro-Differential Operators with Nonsymmetric Positive Kernels: Subcritical Case. Potential Anal 38, 433–455 (2013). https://doi.org/10.1007/s11118-012-9280-2

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  • DOI: https://doi.org/10.1007/s11118-012-9280-2

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