Work

A clustering theorem in fractional Sobolev spaces

Year: 2025

Type: article

Abstract: We prove a general clustering result for the fractional Sobolev space \(W^{s,p}\): whenever the positivity set of a function \(u\) in a cube has measure bounded from below by a multiple of the cube's volume, and the \(W^{s,p}\)-seminorm of \(u\) is bounded from above by a convenient power of the cube's side, then \(u\) is positive in a universally reduced cube. Our result aims at applications in regularity theory for fractional elliptic and parabolic equations. Also, by means of suitable interpolation inequalities, we show that clustering results in \(W^{1,p}\) and \(BV\), respectively, can be deduced as special cases.

Source: Annales Fennici Mathematici

DOI: 10.54330/afm.161328

Authors: Fatma Gamze Düzgün, Antonio Iannizzotto, Vincenzo Vespri

Institutions: University of Cagliari, University of Florence

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

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

Awards: G311438708, G465505792, G5488169599, G755372949