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Spectral Stability for the Peridynamic Fractional p-Laplacian

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Abstract

In this work we analyze the behavior of the spectrum of the peridynamic fractional p-Laplacian, \((-\Delta _p)_{\delta }^{s}\), under the limit process \(\delta \rightarrow 0^+\) or \(\delta \rightarrow +\infty \). We prove spectral convergence to the classical p-Laplacian under a suitable scaling as \(\delta \rightarrow 0^+\) and to the fractional p-Laplacian as \(\delta \rightarrow +\infty \).

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Acknowledgements

This work was carried out while the second author was a postdoctoral researcher at Universidad de Castilla-La Mancha in Ciudad Real funded by project MTM2017-83740-P of the Agencia Estatal de Investigación, Ministerio de Ciencia e Innovación (Spain), which supported this investigation.

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Authors and Affiliations

  1. E.T.S.I. Industriales & INEI, Dpto. de Matemáticas, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain

    José C. Bellido

  2. Dpto. de Matemáticas, Universidad Carlos III de Madrid, Av. de la Universidad 30, 28911, Leganés, Madrid, Spain

    Alejandro Ortega

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  1. José C. Bellido
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  2. Alejandro Ortega
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Correspondence to Alejandro Ortega.

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Bellido, J.C., Ortega, A. Spectral Stability for the Peridynamic Fractional p-Laplacian. Appl Math Optim 84 (Suppl 1), 253–276 (2021). https://doi.org/10.1007/s00245-021-09768-6

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