A remark on nonlocal Neumann conditions for the fractional Laplacian

  • 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.
Metadaten
Author:Nicola AbatangeloORCiD
URN:urn:nbn:de:hebis:30:3-637900
DOI:https://doi.org/10.1007/s00013-020-01440-9
ISSN:1420-8938
Parent Title (English):Archives of mathematics
Parent Title (German):Archiv der Mathematik
Parent Title (French):Archives mathématiques
Publisher:Springer
Place of publication:Berlin ; Heidelberg
Document Type:Article
Language:English
Date of Publication (online):2020/03/12
Date of first Publication:2020/03/12
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2022/07/06
Tag:Fractional Laplacian; Nonlocal Neumann conditions; Nonlocal normal derivative; Regional Laplacian
Volume:114
Issue:6
Page Number:10
First Page:699
Last Page:708
Note:
Open Access funding provided by Projekt DEAL.
HeBIS-PPN:497223708
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J99 None of the above, but in this section
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Sxx Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40] / 35S15 Boundary value problems for pseudodifferential operators
47-XX OPERATOR THEORY / 47Gxx Integral, integro-differential, and pseudodifferential operators [See also 58Jxx] / 47G20 Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx]
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 4.0

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