Article
On the isoperimetric problem in Euclidean space with density
Author/s | Rosales, César
Cañete Martín, Antonio Jesús Bayle, Vincent Morgan, Frank |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2008 |
Deposit Date | 2021-05-26 |
Published in |
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Abstract | We study the isoperimetric problemfor Euclidean space endowedwith a continuous
density. In dimension one, we characterize isoperimetric regions for a unimodal density.
In higher dimensions, we prove existence results and ... We study the isoperimetric problemfor Euclidean space endowedwith a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that for a radial log-convex density, balls about the origin are isoperimetric regions. Finally, we prove this conjecture and the uniqueness of minimizers for the density exp(|x|2) by using symmetrization techniques. |
Funding agencies | Ministerio de Ciencia Y Tecnología (MCYT). España |
Project ID. | MTM2004-01387 |
Citation | Rosales, C., Cañete Martín, A.J., Bayle, V. y Morgan, F. (2008). On the isoperimetric problem in Euclidean space with density. Calculus of Variations and Partial Differential Equations, 31 (1), 27-46. |
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