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Anisotropic fractional Sobolev extension and its applications

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Abstract

In this paper, we show that every function in an anisotropic fractional Sobolev space defined on a regular domain extends to a function defined on the whole \({\mathbb {R}}^n\) with the same Sobolev indices. As an application, we get that such functions are Hölder continuous and we give an explicit estimate for the continuity exponent.

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Acknowledgements

The authors thank the referees very much for valuable suggestions. This work was partially supported by the National Natural Science Foundation of China (12171250 and U21A20426)

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China

    Chengmeng Xu & Wenchang Sun

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  1. Chengmeng Xu
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  2. Wenchang Sun
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Correspondence to Wenchang Sun.

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Communicated by Feng Dai.

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Xu, C., Sun, W. Anisotropic fractional Sobolev extension and its applications. Ann. Funct. Anal. 13, 41 (2022). https://doi.org/10.1007/s43034-022-00184-7

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  • DOI: https://doi.org/10.1007/s43034-022-00184-7

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