On a weighted version of the BBM formula

Fuente: arXiv
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Autore principale: Stefani, Giorgio
Natura: Preprint
Pubblicazione: 2025
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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