We show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regional operator with a kernel having logarithmic behaviour at the boundary.
A remark on nonlocal Neumann conditions for the fractional Laplacian / Abatangelo N.. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - STAMPA. - 114:6(2020), pp. 699-708. [10.1007/s00013-020-01440-9]
A remark on nonlocal Neumann conditions for the fractional Laplacian
Abatangelo N.
2020
Abstract
We show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regional operator with a kernel having logarithmic behaviour at the boundary.File in questo prodotto:
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