Poincaré Inequality on Subanalytic Sets

Let Ω be a subanalytic connected bounded open subset of R n , with possibly singular boundary. We show that given p ∈ [ 1 , ∞ ) , there is a constant C such that for any u ∈ W 1 , p ( Ω ) we have | | u - u Ω | | L p ≤ C | | ∇ u | | L p , where we have set u Ω : = 1 | Ω | ∫ Ω u .

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Veröffentlicht in:	The Journal of Geometric Analysis 2021-10, Vol.31 (10), p.10464-10472
Hauptverfasser:	Valette, Anna, Valette, Guillaume
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Equality Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics
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Beschreibung
Zusammenfassung:	Let Ω be a subanalytic connected bounded open subset of R n , with possibly singular boundary. We show that given p ∈ [ 1 , ∞ ) , there is a constant C such that for any u ∈ W 1 , p ( Ω ) we have \| \| u - u Ω \| \| L p ≤ C \| \| ∇ u \| \| L p , where we have set u Ω : = 1 \| Ω \| ∫ Ω u .
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-021-00652-x