The Bourgain-Brézis-Mironescu formula in arbitrary bounded domains

2020/12/28 by Irene Drelichman, Ricardo G. Durán, Drelichman, Irene +1
Mathematics · #26D10 #46E30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 46E35. Secondary 26A33 #math.AP #msc:26A33 #msc:26D10 #msc:46E30 #msc:46E35.

paper · pdf · doi:10.48550/arxiv.2012.14505

8 pages, simpler proof, new references

arxiv created 2021/01/06 · arxiv updated 2021/01/07

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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