LAUSR

Abstract The paper is about a representation formula introduced by Fusco, Moscariello, and Sbordone in [14] . The formula permits to characterize the gradient norm of a Sobolev function, defined on the whole space , as the limit of non-local energies (BMO-type seminorms) defined on tessellations of generated by cubic cells with arbitrary orientation. We improve the main result in [14] in three different regards: we give a new concise proof of the representation formula, we analyze the case of a generic open subset , and consider general tessellations of Ω by means of cells more general than cubes, again arbitrarily-oriented, inspired by the creative mind of the graphic artist M.C. Escher.