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The Lewy-Stampacchia inequality for the fractional Laplacian and its application to anomalous unidirectional diffusion equations

  • * Corresponding author: Pu-Zhao Kow

    * Corresponding author: Pu-Zhao Kow 

This work was partially supported by JSPS KAKENHI JP20H01812, JP20H00117, JP20KK0058, and MOST 108-2115-M-002-002-MY3

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  • In this paper, we consider a Lewy-Stampacchia-type inequality for the fractional Laplacian on a bounded domain in Euclidean space. Using this inequality, we can show the well-posedness of fractional-type anomalous unidirectional diffusion equations. This study is an extension of the work by Akagi-Kimura (2019) for the standard Laplacian. However, there exist several difficulties due to the nonlocal feature of the fractional Laplacian. We overcome those difficulties employing the Caffarelli-Silvestre extension of the fractional Laplacian.

    Mathematics Subject Classification: 35R11, 35K61, 35K86.


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