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.
A quantitative Sobolev inequality in BV / A. CIANCHI. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 237:(2006), pp. 466-481. [10.1016/j.jfa.2005.12.008]
A quantitative Sobolev inequality in BV
CIANCHI, ANDREA
2006
Abstract
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.
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