The sharp affine $$L^2$$ L 2 Sobolev trace inequality and variants
| Autor: | P. De Nápoli, Julian Haddad, Carlos Hugo Jiménez, Marcos Montenegro |
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| Rok vydání: | 2017 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics Trace (linear algebra) Inequality General Mathematics media_common.quotation_subject 010102 general mathematics Structure (category theory) Centroid 01 natural sciences Sobolev space 0103 physical sciences Euclidean geometry Mathematics::Metric Geometry 010307 mathematical physics Affine transformation 0101 mathematics media_common Mathematics |
| Zdroj: | Mathematische Annalen. 370:287-308 |
| ISSN: | 1432-1807 0025-5831 |
| DOI: | 10.1007/s00208-017-1548-9 |
| Popis: | We establish a sharp affine $$L^p$$ Sobolev trace inequality by using the $$L_p$$ Busemann–Petty centroid inequality. For $$p = 2$$ , our affine version is stronger than the famous sharp $$L^2$$ 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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