Representation of the total variation as a $\Gamma$-limit of \textit{BMO}-type seminorms
(2021) Indiana University Mathematics Journal — Vol. np, n° np, p. 21 (2021)
Files
Arroyo-Representationofthetotal2021.pdf
Open Access - Adobe PDF
- 471.48 KB
Details
- Authors
- et. al.
- Abstract
- We address a question raised by Ambrosio, Bourgain, Brezis, and Figalli, proving that the $\Gamma$-limit, with respect to the $L^1_{\text{loc}}$ topology, of a family of \textit{BMO}-type seminorms is given by $\frac{1}{4}$ 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 $L^1_{\text{loc}}$ in terms of the boundedness of the \textit{BMO}-type seminorms.
- Affiliations
Citations
Arroyo Rabasa, A., Del Nin, G., & et al. (2021). Representation of the total variation as a $\Gamma$-limit of \textit{BMO}-type seminorms. Indiana University Mathematics Journal, np(np), 21. https://doi.org/10.48550/arXiv.2112.03832 (Original work published 2021)