The sharp affine L 2 Sobolev trace inequality and variants

The sharp affine L 2 Sobolev trace inequality and variants

We establish a sharp affineLp Sobolev trace inequality by using the Lp Busemann–Petty centroid inequality. For p=2, our affine version is stronger than the famous sharp L2 Sobolev trace inequality proved independently by Escobar and Beckner. Our approach allows also to characterize all extremizers i...

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Veröffentlicht in:Mathematische annalen 2018-01, Vol.370 (1), p.287-308
Hauptverfasser: De Nápoli, P L, Haddad, J, Jiménez, C H, Montenegro, M
Format: Artikel
Sprache:eng
Schlagworte:
Euclidean geometry
Inequality
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Zusammenfassung:We establish a sharp affineLp Sobolev trace inequality by using the Lp Busemann–Petty centroid inequality. For p=2, our affine version is stronger than the famous sharp L2 Sobolev trace inequality proved independently by Escobar and Beckner. Our approach allows also to characterize all extremizers in this case. For this new inequality, no Euclidean geometric structure is needed.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-017-1548-9