$The Bourgain-Br\'ezis-Mironescu formula in arbitrary bounded domains$

The Bourgain-Br\'ezis-Mironescu formula in arbitrary bounded domains

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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Bibliographische Detailangaben
Veröffentlicht in:	Proceedings of the American Mathematical Society 2022-02, Vol.150 (2), p.701
Hauptverfasser:	Irene Drelichman, Ricardo G. Durán
Format:	Artikel
Sprache:	eng
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/proc/15665