The Besicovitch covering theorem and near-minimizers for the couple (L 2 ; BV)

Let Omega be a rectangle in R-2. A new algorithm for the construction of a near-minimizer for the couple (L-2 (Omega); BV(Omega)) is presented. The algorithm is based on the Besicovitch covering theorem and analysis of local approximations of the given function f is an element of L-2 (Omega).