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Spectral Stability for the Peridynamic Fractional p -Laplacian
Applied Mathematics and Optimization ( IF 1.6 ) Pub Date : 2021-04-02 , DOI: 10.1007/s00245-021-09768-6 José C. Bellido , Alejandro Ortega
中文翻译:
周动力分数p-Laplacian的谱稳定性
更新日期:2021-04-02
Applied Mathematics and Optimization ( IF 1.6 ) Pub Date : 2021-04-02 , DOI: 10.1007/s00245-021-09768-6 José C. Bellido , Alejandro Ortega
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 \(\delta \rightarrow +\infty \).
中文翻译:
周动力分数p-Laplacian的谱稳定性
在这项工作中,我们分析了极限过程\(\ delta \ rightarrow 0 ^下的近动态分数p -Laplacian \((-\ Delta _p)_ {\ delta} ^ {s} \)的光谱行为。+ \)或\(\ delta \ rightarrow + \ infty \)。我们证明了在适当缩放下经典p -Laplacian的谱收敛为\(\ delta \ rightarrow 0 ^ + \),分数p -Laplacian的谱收敛为\(\ delta \ rightarrow + \ infty \)。