Sala Seminari (Dip. Matematica).
In this talk we introduce a notion of functions of fractal bounded variation. Here, the sup-norm of test functions as used in the classical definition is replaced by the Hoelder norm with respect to some exponent. Characteristic functions of domains with fractal bounderies are particular examples that belong to this class. Among a characterization in terms of currents, we state some properties that naturally extend those of classical BV functions such as higher integrability, decomposition into Hoelder functions and push forwards.