# Representation of the total variation as a $\Gamma$-limit of $BMO$-type seminorms

@inproceedings{ArroyoRabasa2021RepresentationOT, title={Representation of the total variation as a \$\Gamma\$-limit of \$BMO\$-type seminorms}, author={Adolfo Arroyo-Rabasa and Paolo Bonicatto and Giacomo Del Nin}, year={2021} }

We address a question raised by Ambrosio, Bourgain, Brezis, and Figalli, proving that the Γ-limit, with respect to the Lloc topology, of a family of BMO-type seminorms is given by 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 Lloc in terms of the boundedness of the BMO-type seminorms. MSC (2020): 26B30, 26D10 (primary); 26A45, 49J45 (secondary).

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