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Representation of the total variation as a Γ-limit of BMO-type seminorms
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Arroyo-Rabasa, Adolfo, Bonicatto, Paolo and Del Nin, Giacomo (2022) Representation of the total variation as a Γ-limit of BMO-type seminorms. Indiana University Mathematical Journal . ISSN 0022-2518. (In Press)
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Abstract
We address a question raised by Ambrosio, Bourgain, Brezis, and Figalli, proving that the $\Gamma$-limit, with respect to the $L^1_{loc}$ topology, of a family of $BMO$-type seminorms is given by $\tfrac14$ times the total variation seminorm. Our method also yields an alternative proof of previously known lower bounds for the pointwise limit and conveys a compactness result in $L^1_{loc}$ in terms of the boundedness of the $BMO$-type seminorms.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | Indiana University Mathematical Journal | ||||||
| Publisher: | Indiana University * Department of Mathematics | ||||||
| ISSN: | 0022-2518 | ||||||
| Official Date: | 2022 | ||||||
| Dates: |
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| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 20 October 2022 | ||||||
| Funder: | ERC grant number 757254, Fonds de la recherche scientifique FNRS 40005112 | ||||||
| Grant number: | 757254 | ||||||
| Related URLs: | |||||||
| Open Access Version: |
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