A Brezis-Nirenberg type result for mixed local and nonlocal operators
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910912857767936 |
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| author | Biagi, Stefano Dipierro, Serena Valdinoci, Enrico Vecchi, Eugenio |
| author_facet | Biagi, Stefano Dipierro, Serena Valdinoci, Enrico Vecchi, Eugenio |
| contents | We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_07502 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Brezis-Nirenberg type result for mixed local and nonlocal operators Biagi, Stefano Dipierro, Serena Valdinoci, Enrico Vecchi, Eugenio Analysis of PDEs We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem. |
| title | A Brezis-Nirenberg type result for mixed local and nonlocal operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2209.07502 |