Recovering functions via doubly homogeneous nonlocal gradients

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.

Authors

Augusto C. Ponce (ORCID: https://orcid.org/0000-0003-2413-1075)
Stefano Buccheri (ORCID: https://orcid.org/0000-0002-0667-233X)

Publication Details

Journal: Comptes Rendus Mathématique
Published: 2025-11-03
DOI: https://doi.org/10.5802/crmath.800
Primary Topic: Nonlinear Partial Differential Equations
Type: article
Field-Weighted Citation Impact: 0.00

Funders

Istituto Nazionale di Alta Matematica "Francesco Severi"
Austrian Science Fund
Fonds De La Recherche Scientifique - FNRS

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article

Recovering functions via doubly homogeneous nonlocal gradients

Augusto C. Ponce, Stefano Buccheri

Nov 3, 2025

Comptes Rendus Mathématique

Nonlinear Partial Differential Equations

article

Recovering functions via doubly homogeneous nonlocal gradients

Augusto C. Ponce, Stefano Buccheri

November 3, 2025article en

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.

Comptes Rendus MathématiqueVol. 363(G12)

Istituto Nazionale di Alta Matematica "Francesco Severi", Austrian Science Fund, Fonds De La Recherche Scientifique - FNRS

Openalex Percentile: Top 55%

Nonlinear Partial Differential Equations

DOI Open Access PDF OpenAlex

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Recovering functions via doubly homogeneous nonlocal gradients — Augusto C. Ponce, Stefano Buccheri · Comptes Rendus Mathématique (2025) | TGRS Research Map | TGRS