On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign''
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917196121243648 |
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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. The main novelty is that we consider a mixed operator of the form $-Δ- γ(-Δ)^s$, namely we suppose that the fractional Laplacian has the ``wrong sign'' and can be seen as a nonlocal perturbation of the purely local case, which is needed to produce a nontrivial solution of the critical problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign'' 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. The main novelty is that we consider a mixed operator of the form $-Δ- γ(-Δ)^s$, namely we suppose that the fractional Laplacian has the ``wrong sign'' and can be seen as a nonlocal perturbation of the purely local case, which is needed to produce a nontrivial solution of the critical problem. |
| title | On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign'' |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.07521 |