Low eigenvalues of the $p-$Laplacian in general open sets
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866915814478708736 |
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| author | Brasco, Lorenzo Briani, Luca Prinari, Francesca |
| author_facet | Brasco, Lorenzo Briani, Luca Prinari, Francesca |
| contents | We consider the minmax Ljusternik-Schnirelmann levels of the constrained $p-$Dirichlet integral, on a general open set of the Euclidean space. We show that, whenever one of these levels lies below the threshold given by the $L^p$ Poincaré constant ``at infinity'', it actually defines an eigenvalue of the Dirichlet $p-$Laplacian. We also prove an exponential decay at infinity for the relevant eigenfunctions: this can be seen as a Šnol-Simon--type estimate for the nonlinear case. Finally, we exhibit some peculiar examples of unbounded open sets to which our main result applies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21118 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Low eigenvalues of the $p-$Laplacian in general open sets Brasco, Lorenzo Briani, Luca Prinari, Francesca Analysis of PDEs Spectral Theory We consider the minmax Ljusternik-Schnirelmann levels of the constrained $p-$Dirichlet integral, on a general open set of the Euclidean space. We show that, whenever one of these levels lies below the threshold given by the $L^p$ Poincaré constant ``at infinity'', it actually defines an eigenvalue of the Dirichlet $p-$Laplacian. We also prove an exponential decay at infinity for the relevant eigenfunctions: this can be seen as a Šnol-Simon--type estimate for the nonlinear case. Finally, we exhibit some peculiar examples of unbounded open sets to which our main result applies. |
| title | Low eigenvalues of the $p-$Laplacian in general open sets |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2602.21118 |