On a sharp inequality of Adimurthi-Druet type and extremal functions
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929295616638976 |
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| author | de Oliveira, José Francisco Ó, João Marcos do |
| author_facet | de Oliveira, José Francisco Ó, João Marcos do |
| contents | Our main purpose in this paper is to establish the existence and nonexistence of extremal functions for sharp inequality of Adimurthi-Druet type for fractional dimensions on the entire space. Precisely, we extend the sharp Trudinger-Moser type inequality in (Calc.Var.Partial Differential Equations, \textbf{52} (2015) 125-163) for the entire space. In addition, we perform the two-step strategy of Carleson-Chang together blow up analysis method to ensure the existence of maximizers for the associated extremal problems for both subcritical and critical regimes. We also present a nonexistence result under subcritical regime for some special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_14181 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a sharp inequality of Adimurthi-Druet type and extremal functions de Oliveira, José Francisco Ó, João Marcos do Analysis of PDEs 35J20, 46E35, 26D10, 35B33 Our main purpose in this paper is to establish the existence and nonexistence of extremal functions for sharp inequality of Adimurthi-Druet type for fractional dimensions on the entire space. Precisely, we extend the sharp Trudinger-Moser type inequality in (Calc.Var.Partial Differential Equations, \textbf{52} (2015) 125-163) for the entire space. In addition, we perform the two-step strategy of Carleson-Chang together blow up analysis method to ensure the existence of maximizers for the associated extremal problems for both subcritical and critical regimes. We also present a nonexistence result under subcritical regime for some special cases. |
| title | On a sharp inequality of Adimurthi-Druet type and extremal functions |
| topic | Analysis of PDEs 35J20, 46E35, 26D10, 35B33 |
| url | https://arxiv.org/abs/2203.14181 |