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Regularity results for fully nonlinear parabolic integro-differential operators

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In this paper, we consider the regularity theory for fully nonlinear parabolic integro-differential equations with symmetric kernels. We are able to find parabolic versions of Alexandrov–Backelman–Pucci estimate with \(0<\sigma <2\). And we show a Harnack inequality, Hölder regularity, and \(C^{1,\alpha }\)-regularity of the solutions by obtaining decay estimates of their level sets.

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Acknowledgments

Ki-ahm Lee has been supported by the Korea-Sweden Research Cooperation Program. This project is part of an STINT (Sweden)-NRF (Korea) research cooperation program.

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Authors and Affiliations

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

    Yong-Cheol Kim

  2. Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Republic of Korea

    Ki-Ahm Lee

  3. School of Mathematics, Korea Institute for Advanced Study, Seoul, 130-722, Republic of Korea

    Ki-Ahm Lee

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

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Kim, YC., Lee, KA. Regularity results for fully nonlinear parabolic integro-differential operators. Math. Ann. 357, 1541–1576 (2013). https://doi.org/10.1007/s00208-013-0948-8

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  • DOI: https://doi.org/10.1007/s00208-013-0948-8

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