Year: 2025
Type: article
Abstract: We investigate a class of nonlocal gradients featuring distinct homogeneities at zero and infinity. We establish a representation formula for such doubly homogeneous operators and derive associated Sobolev-type inequalities. We also propose open questions linked to our results, suggesting directions for future research inspired by the work of Haïm Brezis.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.800
Authors: Stefano Buccheri, Augusto C. Ponce
Institutions: University of Naples Federico II, UCLouvain
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415805680