On the isoperimetric problem with double density. (December 2018)

• Record Type: Journal Article
• Authors: Pratelli, Aldo; Saracco, Giorgio
• Is Part Of: Nonlinear analysis. Volume 177(2018)Part B
• Page Start: 733
• Page End: 752
• Publication Date: 2018-12
• Subjects: primary 49Q10 -- secondary 58B20 49Q20; Isoperimetric problem -- Anisotropic perimeter; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.04.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the isoperimetric problem with double density in Euclidean space; that is, we study the minimisation of the perimeter among subsets of R n with fixed volume, where volume and perimeter are relative to two different densities. The case of a single density, or equivalently, when the two densities coincide, has been well studied in the last years; nonetheless, the problem with two different densities is an important generalisation, also in view of applications. We will prove the existence of isoperimetric sets in this context, extending the known results for the case of single density.