<div class="csl-bib-body">
<div class="csl-entry">Davoli, E., Di Fratta, G., & Pagliari, V. (2024). Sharp conditions for the validity of the Bourgain–Brezis–Mironescu formula. <i>PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS</i>. https://doi.org/10.1017/prm.2024.47</div>
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dc.identifier.issn
0308-2105
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/209202
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dc.description.abstract
Following the seminal paper by Bourgain, Brezis, and Mironescu, we focus on the asymptotic behaviour of some nonlocal functionals that, for each, are defined as the double integrals of weighted, squared difference quotients of. Given a family of weights, we devise sufficient and necessary conditions on for the associated nonlocal functionals to converge as to a variant of the Dirichlet integral. Finally, some comparison between our result and the existing literature is provided.
en
dc.language.iso
en
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dc.publisher
CAMBRIDGE UNIV PRESS
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dc.relation.ispartof
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
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dc.subject
Bourgain-Brezis-Mironescu formula
en
dc.subject
fractional kernels
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dc.subject
Gagliardo seminorm
en
dc.subject
nonlocal functionals
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dc.subject
Radon measures
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dc.title
Sharp conditions for the validity of the Bourgain–Brezis–Mironescu formula
