We prove that the family of functionals defined by for and , -converges in , as goes to zero, when . Hereafter denotes the Euclidean norm of . We also introduce a characterization for bounded variation (BV) functions which has some advantages in comparison with the classic one based on the notion of essential variation on almost every line.
Hoai-Minh Nguyen. "-convergence, Sobolev norms, and BV functions." Duke Math. J. 157 (3) 495 - 533, 15 April 2011. https://doi.org/10.1215/00127094-1272921