On extremizers for Strichartz estimates for higher order Schrödinger equations
| Autor: | René Quilodrán, Diogo Oliveira e Silva |
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| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics Computer Science::Digital Libraries 01 natural sciences Schrödinger equation symbols.namesake Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs 0103 physical sciences Computer Science::Mathematical Software symbols Applied mathematics Order (group theory) 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 370:6871-6907 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/7223 |
| Popis: | For an appropriate class of convex functions $\phi$, we study the Fourier extension operator on the surface $\{(y, |y|^2+\phi(y)):y\in\mathbb{R}^2\}$ equipped with projection measure. For the corresponding extension inequality, we compute optimal constants and prove that extremizers do not exist. The main tool is a new comparison principle for convolutions of certain singular measures that holds in all dimensions. Using tools of concentration-compactness flavor, we further investigate the behavior of general extremizing sequences. Our work is directly related to the study of extremizers and optimal constants for Strichartz estimates of certain higher order Schr\"odinger equations. In particular, we resolve a dichotomy from the recent literature concerning the existence of extremizers for a family of fourth order Schr\"odinger equations, and compute the corresponding operator norms exactly where only lower bounds were previously known. Comment: 39 pages, 1 figure; v2: typos corrected |
| Databáze: | OpenAIRE |
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