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Regularity Theory for Second Order Integro-PDEs

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Abstract

This paper is concerned with higher Hölder regularity for viscosity solutions to non-translation invariant second order integro-PDEs, compared to Mou (2018). We first obtain C1,α regularity estimates for fully nonlinear integro-PDEs. We then prove the Schauder estimates for solutions if the equation is convex.

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Acknowledgements

We would like to thank Andrzej Swiech for helpful discussions and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, CA, USA

    Chenchen Mou

  2. Department of Mathematics, University of California, San Diego, CA, USA

    Yuming Paul Zhang

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  1. Chenchen Mou
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  2. Yuming Paul Zhang
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Correspondence to Yuming Paul Zhang.

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Mou, C., Zhang, Y.P. Regularity Theory for Second Order Integro-PDEs. Potential Anal 54, 387–407 (2021). https://doi.org/10.1007/s11118-020-09831-x

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