The Cheeger problem consists in minimizing the ratio "perimeter over volume" among subsets of a given, bounded domain. This problem has connections with several variational problems (eigenvalue estimates, prescribed mean curvature, Total Variation minimization, and others). After introducing the problem, we will focus on properties of Cheeger sets (i.e., solutions of the above minimization problem) with special emphasis on the two dimensional case. In particular, we shall present some recent results obtained in collaboration with A. Pratelli, on the characterization of Cheeger sets in non-convex, planar domains.

An overview on the Cheeger problem / Leonardi, Gian Paolo. - ELETTRONICO. - 166:(2015), pp. 117-139. (Intervento presentato al convegno New Trends in Shape Optimization tenutosi a Erlangen, Germania nel 23-27 settembre 2013) [10.1007/978-3-319-17563-8_6].

An overview on the Cheeger problem

Leonardi Gian Paolo
2015-01-01

Abstract

The Cheeger problem consists in minimizing the ratio "perimeter over volume" among subsets of a given, bounded domain. This problem has connections with several variational problems (eigenvalue estimates, prescribed mean curvature, Total Variation minimization, and others). After introducing the problem, we will focus on properties of Cheeger sets (i.e., solutions of the above minimization problem) with special emphasis on the two dimensional case. In particular, we shall present some recent results obtained in collaboration with A. Pratelli, on the characterization of Cheeger sets in non-convex, planar domains.
2015
New Trends in Shape Optimization
DEU
Birkhauser / Springer
9783319175638
Leonardi, Gian Paolo
An overview on the Cheeger problem / Leonardi, Gian Paolo. - ELETTRONICO. - 166:(2015), pp. 117-139. (Intervento presentato al convegno New Trends in Shape Optimization tenutosi a Erlangen, Germania nel 23-27 settembre 2013) [10.1007/978-3-319-17563-8_6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/229192
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