Academic Journal
On the sharp constant in the Bianchi–Egnell stability inequality: On the sharp constant in the Bianchi-Egnell stability inequality
| Τίτλος: | On the sharp constant in the Bianchi–Egnell stability inequality: On the sharp constant in the Bianchi-Egnell stability inequality |
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| Συγγραφείς: | König, Tobias |
| Πηγή: | Bulletin of the London Mathematical Society. 55:2070-2075 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Wiley, 2023. |
| Έτος έκδοσης: | 2023 |
| Θεματικοί όροι: | Mathematics - Analysis of PDEs, Bianchi-Egnell inequality, Sobolev inequality, FOS: Mathematics, Inequalities involving derivatives and differential and integral operators, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, 01 natural sciences, fractional exponents, Analysis of PDEs (math.AP) |
| Περιγραφή: | This note is concerned with the Bianchi–Egnell inequality, which quantifies the stability of the Sobolev inequality, and its generalization to fractional exponents . We prove that in dimension the best constant is strictly smaller than the spectral gap constant associated to sequences that converge to the manifold of Sobolev optimizers. In particular, cannot be asymptotically attained by such sequences. Our proof relies on a precise expansion of the Bianchi–Egnell quotient along a well‐chosen sequence of test functions converging to . |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1469-2120 0024-6093 |
| DOI: | 10.1112/blms.12837 |
| DOI: | 10.48550/arxiv.2210.08482 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2210.08482 |
| Rights: | CC BY NC arXiv Non-Exclusive Distribution |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....546b3d0e5cda692045d6c4beb47f92cb |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 14692120 00246093 |
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| DOI: | 10.1112/blms.12837 |