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Interior Regularity for Regional Fractional Laplacian

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Abstract

In this paper, we study interior regularity properties for the regional fractional Laplacian operator. We obtain the integer order differentiability of the regional fractional Laplacian, which solves a conjecture of Guan and Ma (Probab. Theory Related Fields 134:649–694, 2006). We further extend the integer order differentiability to the fractional order of the regional fractional Laplacian. Schauder estimates for the regional fractional Laplacian are also provided.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Chenchen Mou & Yingfei Yi

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Yingfei Yi

  3. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Yingfei Yi

Authors
  1. Chenchen Mou
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  2. Yingfei Yi
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Corresponding author

Correspondence to Chenchen Mou.

Additional information

Communicated by L. Caffarelli

This research was partially supported by NSF Grant DMS1109201. Y. Yi was also supported by a NSERC discovery grant, a scholarship from Jilin University, and a faculty development fund from the University of Alberta.

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Mou, C., Yi, Y. Interior Regularity for Regional Fractional Laplacian. Commun. Math. Phys. 340, 233–251 (2015). https://doi.org/10.1007/s00220-015-2445-2

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  • DOI: https://doi.org/10.1007/s00220-015-2445-2

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