Struwe's Global Compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909707036262400 |
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| author | Palatucci, Giampiero Piccinini, Mirco Temperini, Letizia |
| author_facet | Palatucci, Giampiero Piccinini, Mirco Temperini, Letizia |
| contents | We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorgi's $Γ$-convergence techniques that optimal functions for a natural subcritical approximations of the Sobolev quotient concentrate energy at one point. In the second part of the paper, we try to restore the compactness by extending the celebrated Global Compactness result to the Heisenberg group via a completely different approach with respect to the original one by Struwe [37]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01153 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Struwe's Global Compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group Palatucci, Giampiero Piccinini, Mirco Temperini, Letizia Analysis of PDEs We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorgi's $Γ$-convergence techniques that optimal functions for a natural subcritical approximations of the Sobolev quotient concentrate energy at one point. In the second part of the paper, we try to restore the compactness by extending the celebrated Global Compactness result to the Heisenberg group via a completely different approach with respect to the original one by Struwe [37]. |
| title | Struwe's Global Compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2308.01153 |