The Bourgain-Brézis-Mironescu formula in arbitrary bounded domains

preprint2021arXivOpen access

Abstract

We obtain a Bourgain-Brézis-Mironescu formula on the limit behaviour of a modified fractional Sobolev seminorm when s↗1s\nearrow 1, which is valid in arbitrary bounded domains. In the case of extension domains, we recover the classical result.

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