Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929248488390656 |
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| author | Gobbino, Massimo Picenni, Nicola |
| author_facet | Gobbino, Massimo Picenni, Nicola |
| contents | We consider a family of non-local and non-convex functionals, and we prove that their Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total variation. As a by-product, we answer some open questions concerning the limiting behavior of these functionals.
The proof relies on the analysis of a discretized version of these functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05560 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms Gobbino, Massimo Picenni, Nicola Functional Analysis 49J45, 26D10, 46E35, 26B30 We consider a family of non-local and non-convex functionals, and we prove that their Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total variation. As a by-product, we answer some open questions concerning the limiting behavior of these functionals. The proof relies on the analysis of a discretized version of these functionals. |
| title | Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms |
| topic | Functional Analysis 49J45, 26D10, 46E35, 26B30 |
| url | https://arxiv.org/abs/2311.05560 |