A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
Cc BY
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s42985-023-00232-4 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7526 |
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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 |
| _version_ |
1762365498925776896 |
| score |
8.891695 |