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This document discusses the classical Sobolev inequality and presents a theorem regarding the relationship between the Sobolev norm and the distance to a manifold of extremal functions. The authors prove that there exists a positive constant such that the inequality holds, and they provide a sharp result that addresses a question posed by Brezis and Lieb. Additionally, the document includes alternative proofs and related results in the context of Sobolev spaces.

Author

Frankie Frankie

Language

EN