arXiv:2308.12830 Abstract | arXiv Analytics

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Bougain-Brezis-Mironescu formula for Triebel-Lizorkin spaces in arbitrary domains

Published 2023-08-24Version 1

We show that the Bourgain-Brezis-Mironescu formula, regarding the limits of Gagliardo-type seminorms as $s\to 1-$, holds for Triebel-Lizorkin spaces defined in arbitrary domains. This answers an open question raised by Brazke-Schikorra-Yung in [Bourgain-Brezis-Mironescu convergence via Triebel-Lizorkin spaces; Calc. Var. Partial Differential Equations; 2023].

Categories: math.FA, math.AP

Subjects: 46E35, 42B35

Keywords: triebel-lizorkin spaces, arbitrary domains, bougain-brezis-mironescu formula, partial differential equations, gagliardo-type seminorms

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