A quantitative Sobolev inequality in BV

摘要

A quantitative version of the standard Sobolev inequality, with sharp constant, for functions u in W-1,W-1 (R-n) (or BV(R-n)) is established in terms of a distance of u from the manifold of all multiples of characteristic functions of balls. Inequalities involving non-Euclidean norms of the gradient are discussed as well. (C) 2005 Elsevier Inc. All rights reserved.