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math.AP2016
The Maz'ya-Shaposhnikova limit in the magnetic setting
Andrea Pinamonti, Marco Squassina, Eugenio Vecchi
We prove a magnetic version of the Maz'ya-Shaposhnikova singular limit of nonlocal norms with vanishing fractional parameter. This complements a general convergence result recently…
math.AP2016
Magnetic BV functions and the Bourgain-Brezis-Mironescu formula
Andrea Pinamonti, Marco Squassina, Eugenio Vecchi
We prove a general magnetic Bourgain-Brezis-Mironescu formula. In particular, after developing a theory of magnetic bounded variation functions, we prove the validity of the formul…