On the isoperimetric problem with double density

DOI10.1016/j.na.2018.04.009zbMath1403.49044arXiv1804.02966OpenAlexW2795405153WikidataQ129860058 ScholiaQ129860058MaRDI QIDQ1627440

Giorgio Saracco, Aldo Pratelli

Publication date: 22 November 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.02966

zbMATH Keywords

isoperimetric problemanisotropic perimeter

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20)

Related Items (15)

Isoperimetric clusters in homogeneous spaces via concentration compactness ⋮ On the Steiner property for planar minimizing clusters. The isotropic case ⋮ The isoperimetric problem in the Heisenberg group \(\mathbb{H}^n\) with density ⋮ A formula for the minimal perimeter of clusters with density ⋮ Optimal regularity of isoperimetric sets with Hölder densities ⋮ On the Steiner property for planar minimizing clusters. The anisotropic case ⋮ Some weighted isoperimetric inequalities in quantitative form ⋮ Unnamed Item ⋮ A nonlocal isoperimetric problem with density perimeter ⋮ Total Variation Isoperimetric Profiles ⋮ A discrete districting plan ⋮ Isoperimetric inequalities in cylinders with density ⋮ The \(\varepsilon - \varepsilon^\beta\) property in the isoperimetric problem with double density, and the regularity of isoperimetric sets ⋮ Some isoperimetric inequalities with respect to monomial weights ⋮ Minimizers of the prescribed curvature functional in a Jordan domain with no necks

Cites Work

• Unnamed Item
• Isoperimetric regions in \(\mathbb R^{n}\) with density \(r^{p}\)
• Euclidean balls solve some isoperimetric problems with nonradial weights
• Some isoperimetric problems in planes with density
• Weighted Cheeger sets are domains of isoperimetry
• Existence of isoperimetric regions in \(\mathbb{R}^{n}\) with density
• Existence of isoperimetric sets with densities ``converging from below on \({\mathbb {R}}^N\)
• On the isoperimetric problem in Euclidean space with density
• Isoperimetric problems in sectors with density

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