A surprising formula for Sobolev norms
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Brezis, Haim
Van Schaftingen, Jean
Yung, Po-Lam
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National Academy of Sciences (USA)
Abstract
We establish the equivalence between the Sobolev seminorm k∇ukLp and a quantity obtained when replacing strong Lp by weak Lp in the Gagliardo seminorm |u|Ws,p computed at s = 1. As corollaries we derive alternative estimates in some exceptional cases (involving W1,1) where the “anticipated” fractional Sobolev and Gagliardo–Nirenberg inequalities fail.
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PNAS - Proceedings of the National Academy of Sciences of the United States of America
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Restricted until
2099-12-31
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