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Annals of Global Analysis and Geometry

, Volume 43, Issue 4, pp 331–365 | Cite as

Existence of isoperimetric regions in \({\mathbb{R}^{n}}\) with density

  • Frank Morgan
  • Aldo PratelliEmail author
Article

Abstract

We prove the existence of isoperimetric regions in \({\mathbb{R}^{n}}\) with density under various hypotheses on the growth of the density. Along the way, we prove results on the boundedness of isoperimetric regions.

Keywords

Isoperimetric sets \({\mathbb{R}^{n}}\) with density Existence of optimal sets Boundedness of optimal sets 

Mathematics Subject Classification

Primary 49Q05 Secondary 53A10 49Q20 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsWilliams CollegeWilliamstownUSA
  2. 2.Dipartimento di MatematicaUniversità di Pavia “F. Casorati”PaviaItaly

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