Abstract
In this note, we study the asymptotic behavior of eigenvalues and eigenfunctions of the regional fractional Laplacian \((-{\Delta })^{s}_{\Omega }\) as \(s\rightarrow 0^{+}.\) Our analysis leads to a study of the regional logarithmic Laplacian, which arises as a formal derivative of regional fractional Laplacians at s = 0.
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Acknowledgements
This work is supported by DAAD and BMBF (Germany) within the project 57385104. The authors would like to thank Mouhamed Moustapha Fall and Sven Jarohs for valuable discussions. They also would like to thank the referee for his/her corrections.
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Open Access funding enabled and organized by Projekt DEAL. This work is supported by DAAD and BMBF (Germany) within the project 57385104.
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Temgoua, R.Y., Weth, T. The Eigenvalue Problem for the Regional Fractional Laplacian in the Small Order Limit. Potential Anal 60, 285–306 (2024). https://doi.org/10.1007/s11118-022-10050-9
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DOI: https://doi.org/10.1007/s11118-022-10050-9
Keywords
- Regional fractional Laplacian
- Regional logarithmic Laplacian
- Asymptotic behavior
- Eigenfunctions
- Eigenvalues