Work

On a weighted version of the BBM formula

Year: 2025

Type: article

Abstract: 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 ∞ 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.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2025.130272

Author: Giorgio Stefani

Institution: University of Padua

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190