Ortega García, Alejandro2025-03-312025-03-312025-06-01Alejandro Ortega. “Pervasiveness of the p-Laplace operator under localization of fractional g-Laplace operators”, J. Nonlinear Var. Anal. 9 (2025), 373-395. https://doi.org/10.23952/jnva.9.2025.3.042560-6921; e-ISSN: 2560-6778https://doi.org/10.23952/jnva.9.2025.3.04https://hdl.handle.net/20.500.14468/26402Esta es la versión aceptada para su publicación en Journal of Nonlinear and Variational Analysis 9 (2025), 373-395. La versión final publicada está disponible en la web del editor: Biemdas Academic Publishers: https://doi.org/10.23952/jnva.9.2025.3.04. This is the accepted version for publication in Journal of Nonlinear and Variational Analysis 9 (2025), 373–395. The final published version is available on the publisher's website: Biemdas Academic Publishers: https://doi.org/10.23952/jnva.9.2025.3.04.In this paper, we analyze the behavior of the truncated functionals as (Formula presented) for δ → 0+, where G is an Orlicz function which is assumed to be regularly varying at 0. A prototype of such function is given by G(t) = tp(1+ |log(t)|) with p ≥ 2. These kinds of functionals arise naturally in peridynamics, where long-range interactions are neglected and only those that exerted at distance smaller than δ > 0 are taken into account, i.e., the horizon δ > 0 represents the range of interactions or nonlocality. This paper is inspired by the celebrated result by Bourgain, Brezis and Mironescu, who analyzed the limit s → 1− with G(t) = tp. In particular, we prove that, under appropriate conditions, (Formula presented) for p = index(G) and an explicit constant KN,p > 0. Moreover, the converse is also true if the above localization limit exist as δ → 0+, and the Orlicz function G is a regularly varying function with index(G) = p.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículo