Short proofs of refined sharp Caffarelli-Kohn-Nirenberg inequalities
| Autor: | Cristian Cazacu, Nguyen Lam, Joshua Flynn |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Inequality Applied Mathematics media_common.quotation_subject 010102 general mathematics 81S07 26D10 46E35 26D15 Mathematical proof 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis 010101 applied mathematics Mathematics - Analysis of PDEs FOS: Mathematics 0101 mathematics Nirenberg and Matthaei experiment Analysis Analysis of PDEs (math.AP) Mathematics media_common |
| Zdroj: | Journal of Differential Equations. 302:533-549 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2021.09.005 |
| Popis: | This note relies mainly on a refined version of the main results of the paper by F. Catrina and D. Costa (J. Differential Equations 2009). We provide very short and self-contained proofs. Our results are sharp and minimizers are obtained in suitable functional spaces. As main tools we use the so-called \textit{expand of squares} method to establish sharp weighted $L^{2}$-Caffarelli-Kohn-Nirenberg (CKN) inequalities and density arguments. Comment: 13 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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