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In this chapter, we present several equivalent definitions of the fractional Laplacian, discuss its basic properties, asymptotic behavior, and useful identities, as well as its behavior under point inversion (Kelvin transform), the exchange of the order of differentials, and the special case of periodic functions. En passant, we also recall a nonlocal representation of the classical Laplacian.

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Equivalent Definitions of the Fractional Laplacian

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  • 发表日期：

    2025年

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  • Nicola Abatangelo,
  • Serena Dipierro,
  • Enrico Valdinoci

摘要

In this chapter, we present several equivalent definitions of the fractional Laplacian, discuss its basic properties, asymptotic behavior, and useful identities, as well as its behavior under point inversion (Kelvin transform), the exchange of the order of differentials, and the special case of periodic functions. En passant, we also recall a nonlocal representation of the classical Laplacian.