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On the fractional Laplacian of variable order

Technical Report ·
DOI:https://doi.org/10.2172/1821967· OSTI ID:1821967
 [1];  [2];  [3];  [4];  [1]
  1. Stanford Univ., CA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  3. Univ. of Bari Aldo Moro (Italy)
  4. Eidgenoessische Technische Hochschule (ETH), Zurich (Switzerland)

We present a novel definition of variable-order fractional Laplacian on Rn based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson’s equation involving this operator and we compute the corresponding Green’s function, for which we provide some instructive examples for specific problems.

Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
DOE Contract Number:
NA0003525
OSTI ID:
1821967
Report Number(s):
SAND2021-10850R; 699959
Country of Publication:
United States
Language:
English

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