We introduce the space SBV_X of special functions with bounded X-variation in Carnot–Carathéodory spaces and study its main properties. Our main outcome is an approximation result, with respect to the BV_X topology, for SBV_X functions.
SBV functions in Carnot–Carathéodory spaces
Di Marco, Marco;Vittone, Davide
2026
Abstract
We introduce the space SBV_X of special functions with bounded X-variation in Carnot–Carathéodory spaces and study its main properties. Our main outcome is an approximation result, with respect to the BV_X topology, for SBV_X functions.
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