Academic Journal
On the sharp constant in the Bianchi–Egnell stability inequality: On the sharp constant in the Bianchi-Egnell stability inequality
| Title: | On the sharp constant in the Bianchi–Egnell stability inequality: On the sharp constant in the Bianchi-Egnell stability inequality |
|---|---|
| Authors: | König, Tobias |
| Source: | Bulletin of the London Mathematical Society. 55:2070-2075 |
| Publication Status: | Preprint |
| Publisher Information: | Wiley, 2023. |
| Publication Year: | 2023 |
| Subject Terms: | 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) |
| Description: | 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 . |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1469-2120 0024-6093 |
| DOI: | 10.1112/blms.12837 |
| DOI: | 10.48550/arxiv.2210.08482 |
| Access URL: | http://arxiv.org/abs/2210.08482 |
| Rights: | CC BY NC arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....546b3d0e5cda692045d6c4beb47f92cb |
| Database: | OpenAIRE |
| ISSN: | 14692120 00246093 |
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| DOI: | 10.1112/blms.12837 |