On a weighted version of the BBM formula
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913785932939264 |
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| author | Stefani, Giorgio |
| author_facet | Stefani, Giorgio |
| contents | We prove a weighted version of the Bourgain-Brezis-Mironescu (BBM) formula, both in the pointwise and $Γ$-convergence sense, together with a compactness criterion for energy-bounded sequences. The non-negative weights need only be $L^\infty$ convergent to a bounded and uniformly continuous limit. We apply the BBM formula to show a Poincaré-type inequality and the stability of the first eigenvalues relative to the energies. Finally, we discuss a non-local analogue of the weighted BBM formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a weighted version of the BBM formula Stefani, Giorgio Analysis of PDEs Functional Analysis Primary 46E35. Secondary 26A33, 26D10, 35P30 We prove a weighted version of the Bourgain-Brezis-Mironescu (BBM) formula, both in the pointwise and $Γ$-convergence sense, together with a compactness criterion for energy-bounded sequences. The non-negative weights need only be $L^\infty$ convergent to a bounded and uniformly continuous limit. We apply the BBM formula to show a Poincaré-type inequality and the stability of the first eigenvalues relative to the energies. Finally, we discuss a non-local analogue of the weighted BBM formula. |
| title | On a weighted version of the BBM formula |
| topic | Analysis of PDEs Functional Analysis Primary 46E35. Secondary 26A33, 26D10, 35P30 |
| url | https://arxiv.org/abs/2504.06736 |