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dc.contributor.author
Ceretani, Andrea Noemí  
dc.contributor.author
Rautenberg, Carlos N.  
dc.date.available
2024-05-08T15:36:24Z  
dc.date.issued
2023-10  
dc.identifier.citation
Ceretani, Andrea Noemí; Rautenberg, Carlos N.; The spatially variant fractional Laplacian; Springer; Fractional Calculus and Applied Analysis; 26; 6; 10-2023; 2837-2873  
dc.identifier.issn
1314-2224  
dc.identifier.uri
http://hdl.handle.net/11336/234955  
dc.description.abstract
We introduce a definition of the fractional Laplacian (−Δ)^s(⋅) with spatially variable order s:Ω→[0,1] and study the solvability of the associated Poisson problem on a bounded domain Ω. The initial motivation arises from the extension results of Caffarelli and Silvestre, and Stinga and Torrea; however the analytical tools and approaches developed here are new. For instance, in some cases we allow the variable order s(⋅) to attain the values 0 and 1 leading to a framework on weighted Sobolev spaces with non-Muckenhoupt weights. Initially, and under minimal assumptions, the operator (−Δ)^s(⋅) is identified as the Lagrange multiplier corresponding to an optimization problem; and its domain is determined as a quotient space of weighted Sobolev spaces. The well-posedness of the associated Poisson problem is then obtained for data in the dual of this quotient space. Subsequently, two trace regularity results are established, allowing to partially characterize functions in the aforementioned quotient space whenever a Poincaré type inequality is available. Precise examples are provided where such inequality holds, and in this case the domain of the operator (−Δ)^s(⋅) is identified with a subset of a weighted Sobolev space with spatially variant smoothness s(⋅). The latter further allows to prove the well-posedness of the Poisson problem assuming functional regularity of the data.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Springer  
dc.rights
info:eu-repo/semantics/restrictedAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
FRACTIONAL ORDER SOBOLEV SPACE  
dc.subject
SPATIALLY VARYING EXPONENT  
dc.subject
TRACE THEOREM  
dc.subject
FRACTIONAL LAPLACIAN WITH VARIABLE EXPONENT  
dc.subject
HARDY-TYPE INEQUALITIES  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
The spatially variant fractional Laplacian  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2024-05-03T13:57:33Z  
dc.journal.volume
26  
dc.journal.number
6  
dc.journal.pagination
2837-2873  
dc.journal.pais
Suiza  
dc.description.fil
Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina  
dc.description.fil
Fil: Rautenberg, Carlos N.. George Mason University; Estados Unidos  
dc.journal.title
Fractional Calculus and Applied Analysis  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s13540-023-00212-w  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s13540-023-00212-w