Local clustering of the non-zero set of functions in \(W^{1,1} (E)\)
type: Item
instance of: scholarly article
title: Local clustering of the non-zero set of functions in \(W^{1,1} (E)\)
zbMATH Open document ID: 1223.46034
DOI: 10.4171/RLM/465
author: Emmanuele DiBenedetto
author: Ugo Gianazza
author: Vincenzo Vespri
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2007-08-07T00:00:00Z
review text: Summary: We extend to the \(p=1\) case a measure theoretic result previously proved by \textit{E. DiBenedetto} and \textit{V. Vespri} [Arch. Ration. Mech. Anal. 132, No. 3, 247--309 (1995; Zbl 0849.35060)] for functions that belong to \(u \in W^{1,p} (K_{\rho} (x_{0}))\) where \(K_{\rho} (x_{0})\) is a \(N\)-dimensional cube of edge \(\rho\) centered at \(x_0\). It basically states that if the set where \(u\) is bounded away from zero occupies a seizable portion of \(K_{\rho}\), then the set where \(u\) is positive clusters about at least one point of \(K_{\rho}\).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26B35
zbMATH DE Number: 5177497
zbMATH Keywords: \(W^{1,1} (E)\) functions
zbMATH Keywords: measure theory
zbMATH Keywords: positivity set
MaRDI profile type: Publication
cites work: On the singular equation \(\beta (u)_ t=\Delta u\)
full work available at URL: https://doi.org/10.4171/rlm/465
OpenAlex ID: W1988158511
description: scientific article; zbMATH DE number 5177497