On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density

DOI10.1016/j.jfa.2011.01.007zbMath1222.49058OpenAlexW2059388481MaRDI QIDQ537705

Francesco Maggi, Aldo Pratelli, Nicola Fusco

Publication date: 20 May 2011

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2011.01.007

zbMATH Keywords

isoperimetric problemexistence of minimizersGaussian density

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (15)

The \(\epsilon\)-\(\epsilon^\beta\) property, the boundedness of isoperimetric sets in \(\mathbb{R}^{N}\) with density, and some applications ⋮ Uniqueness results and enclosure properties for hypersurfaces with boundary in weighted cylinders ⋮ Regularity of isoperimetric sets in \(\mathbb R^2\) with density ⋮ On the isoperimetric problem with perimeter density \(r^p\) ⋮ On the isoperimetric problem for radial log-convex densities ⋮ \(L_p\) centroid bodies with respect to weights \(|x|^{\ell}\) ⋮ The ε-ε property and the boundedness of isoperimetric sets with different monomial weights ⋮ Best constants for the isoperimetric inequality in quantitative form ⋮ A nonlocal isoperimetric problem with density perimeter ⋮ Isoperimetric and stable sets for log-concave perturbations of Gaussian measures ⋮ Sharp isoperimetric inequalities via the ABP method ⋮ A fractional isoperimetric problem in the Wiener space ⋮ Isoperimetric inequalities in cylinders with density ⋮ On the existence and nonexistence of isoperimetric inequalities with different monomial weights ⋮ The \(\varepsilon - \varepsilon^\beta\) property in the isoperimetric problem with double density, and the regularity of isoperimetric sets

Cites Work

• Isoperimetric comparison theorems for manifolds with density
• Some isoperimetric problems in planes with density
• Isoperimetric regions in the plane with density \(r^{p}\)
• The Brunn-Minkowski inequality in Gauss space
• On the isoperimetric problem in Euclidean space with density
• On the isoperimetric deficit in Gauss space
• Symétrisation dans l'espace de Gauss.
• THE ISOPERIMETRIC PROBLEM ON PLANES WITH DENSITY
• Regularity of isoperimetric hypersurfaces in Riemannian manifolds
• On the cases of equality in Bobkov's inequality and Gaussian rearrangement
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