Submitted Paper
Inserted: 9 apr 2025
Last Updated: 9 apr 2025
Year: 2025
Abstract:
We prove a weighted version of the Bourgain–Brezis–Mironescu (BBM) formula, both in the pointwise and $\Gamma$-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.
Keywords: Gamma-convergence, Poincare inequality, Compactness, weight, BBM formula, pointwise limit, spectral stability, non-local energy
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