A quantitative Sobolev inequality in BV |
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| Authors: | Andrea Cianchi |
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| Institution: | Dipartimento di Matematica e Applicazioni per l'Architettura, Università di Firenze, Piazza Ghiberti 27, 50122 Firenze, Italy |
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| Abstract: | A quantitative version of the standard Sobolev inequality, with sharp constant, for functions u in W1,1(Rn) (or BV(Rn)) 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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| Keywords: | Sobolev inequalities Isoperimetric inequalities Remainder terms Functions of bounded variation Lorentz spaces |
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