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A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces

Cc BY

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Bibliographic Details
Main Author: Guy Fabrice Foghem, Gounoue
Format: Book
Language:English
Published: Springer 2023
Subjects:
p-Lévy integrable functions
local Radon measures
Online Access:https://link.springer.com/article/10.1007/s42985-023-00232-4
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7526
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spelling oai:localhost:PNK-75262023-04-05T02:27:10Z A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces Guy Fabrice Foghem, Gounoue p-Lévy integrable functions local Radon measures Cc BY We introduce a large class of concentrated p-Lévy integrable functions approximating the unity, which serves as the core tool from which we provide a nonlocal characterization of the Sobolev spaces and the space of functions of bounded variation via nonlocal energies forms. It turns out that this nonlocal characterization is a necessary and sufficient criterion to define Sobolev spaces on domains satisfying the extension property. We also examine the general case where the extension property does not necessarily hold. In the latter case we establish weak convergence of the nonlocal Radon measures involved to the local Radon measures induced by the distributional gradient. 2023-04-05T02:27:10Z 2023-04-05T02:27:10Z 2023 Book https://link.springer.com/article/10.1007/s42985-023-00232-4 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7526 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic p-Lévy integrable functions
local Radon measures
spellingShingle p-Lévy integrable functions
local Radon measures
Guy Fabrice Foghem, Gounoue
A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
description Cc BY
format Book
author Guy Fabrice Foghem, Gounoue
author_facet Guy Fabrice Foghem, Gounoue
author_sort Guy Fabrice Foghem, Gounoue
title A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
title_short A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
title_full A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
title_fullStr A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
title_full_unstemmed A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
title_sort remake of bourgain–brezis–mironescu characterization of sobolev spaces
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s42985-023-00232-4
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7526
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score 8.891695

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