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In this chapter, we present several explicit identities related to the fractional Laplacian, providing examples of fractional harmonic functions and functions that satisfy notable fractional equations. Special geometries of the supporting domain are considered, such as half-spaces, balls, and ellipsoids.

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Some Explicit Calculations of Fractional Laplacians

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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 explicit identities related to the fractional Laplacian, providing examples of fractional harmonic functions and functions that satisfy notable fractional equations. Special geometries of the supporting domain are considered, such as half-spaces, balls, and ellipsoids.