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Regularity for Fully Nonlinear Equations Driven by Spatial-Inhomogeneous Nonlocal Operators

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Abstract

We consider a class of nonlocal operators that are not necessarily spatially homogeneous and impose mild assumptions on its kernel near zero. Furthermore, we prove Hölder regularity for a large class of fully nonlinear integro-differential equations. In particular, the results cover the case when the kernel K(x,y) is comparable to \(|x-y|^{-d-\alpha } \ln \left (|x-y|^{-1}\right )\) for |x−y|<r 0, where 0 < α < 2.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul, 151-747, Republic of Korea

    Jongchun Bae

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  1. Jongchun Bae
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Correspondence to Jongchun Bae.

Additional information

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (NRF-2013R1A2A2A01004822).

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Bae, J. Regularity for Fully Nonlinear Equations Driven by Spatial-Inhomogeneous Nonlocal Operators. Potential Anal 43, 611–624 (2015). https://doi.org/10.1007/s11118-015-9488-z

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