Calculus of Variations and Geometric Measure Theory

G. P. Leonardi - A. Pratelli

On the Cheeger sets in strips and non-convex domains

created by pratelli on 16 Feb 2015
modified by leonardi on 31 Jan 2024


Published Paper

Inserted: 16 feb 2015
Last Updated: 31 jan 2024

Journal: Calc. Var. PDE
Year: 2016

ArXiv: 1409.1376 PDF


In this paper we consider the Cheeger problem for non-convex domains, with a particular interest in the case of planar strips, which have been extensively studied in recent years. Our main results are an estimate on the Cheeger constant of strips, which is stronger than the previous one known from a recent result by D. Krejcirik and the second-named author, and the proof that strips share with convex domains a number of crucial properties with respect to the Cheeger problem. Moreover, we present several counterexamples showing that the same properties are not valid for generic non-convex domains.