Work

Lower bounds and Poincaré inequality for the Brezis-Seeger-Van Schaftingen-Yung functionals

Year: 2026

Type: preprint

Abstract: We consider a family of non-local and non-convex functionals depending on three real parameters $(γ,p,λ)$, which was introduced by H. Brezis, A. Seeger, J. Van Schaftingen and P. L. Yung. In the case $γ<-p$ we prove a lower bound for the Gamma-liminf of these functionals as $λ\to 0^+$ and a Poincaré-type inequality. We also show that such inequality cannot hold if $γ>0$, and we establish a modified version in this case. These results answer some open questions posed by these authors and by H. M. Nguyen.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.05929

Author: Picenni, Nicola

Institution: University of Rome Tor Vergata

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

OpenAlex ID: W7220706678

Cites: 2

Cited by: 1

Related to: 10