BV-Ellipticity and Lower Semicontinuity of Surface Energy of Caccioppoli Partitions of ℝ n

摘要: We give a new proof that BV-ellipticity is sufficient for lower semicontinuity of surface energy Caccioppoli partitions ℝn, any n≥2, with respect to convergence in volume. BV-ellipticity, introduced by L. Ambrosio and A. Braides two decades ago, the only condition known be necessary context ℝn; it analogous, this setting, C.B. Morrey’s quasi-convexity. also show, first time, suffices weaker notions involving weak flat topologies on integral currents.