Some results on powers of the Laplacian between 1 and 2

  • Nicola Abatangelo (Université Libre de Bruxelles)
G3 10 (Lecture hall)


We will review some results --obtained in collaboration with Sven Jarohs (Frankfurt) and Alberto Saldaña (Karlsruhe)-- concerning higher-order fractional Laplacians, which are nonlocal operators of non-integer order larger than 2. These pertain the validity (or rather the failure) of maximum principles, the extension of Boggio's formula for the Green function, the structure and the boundary behaviour of corresponding harmonics, the formulation of suitable natural boundary conditions, and the pointwise evaluation of the operators.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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