The Bourgain-Brézis-Mironescu formula in arbitrary bounded domains

Drelichman, Irene; Durán, Ricardo

doi:10.1090/proc/15665

The Bourgain-Brézis-Mironescu formula in arbitrary bounded domains
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by Irene Drelichman and Ricardo G. Durán PDF

Proc. Amer. Math. Soc. 150 (2022), 701-708 Request permission

Abstract:

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

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