On a weighted version of the BBM formula

Giorgio Stefani

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arXiv · 2504.06736

On a weighted version of the BBM formula

Giorgio Stefani

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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 Poincar\'e-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.

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Giorgio Stefani. 2025-04-09. On a weighted version of the BBM formula. https://arxiv.org/abs/2504.06736

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