Work

A Note on Non-local Sobolev Spaces and Non-local Perimeters

Year: 2025

Type: article

Abstract: We investigate the space of non-local Sobolev functions associated with an integral kernel. We prove an extension result, Sobolev and Poincaré inequalities and an isoperimetric inequality for the non-local perimeter restricted to a set. Finally, we remark on non-local isoperimetric problems, even when the underlying kernel is not necessarily radially symmetric.

Source: La Matematica

DOI: 10.1007/s44007-025-00175-9

Authors: Konstantinos Bessas, Giuseppe Cosma Brusca

Institutions: University of Pavia, Scuola Internazionale Superiore di Studi Avanzati

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Fondazione Cariplo, Università degli Studi di Pavia