On the Cheeger sets in strips and non-convex domains

Leonardi GP, Pratelli A (2016)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2016

Journal

Calculus of Variations and Partial Differential Equations Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 55

Pages Range: 1-28

Article Number: 15

Journal Issue: 1

DOI: 10.1007/s00526-016-0953-3

Abstract

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 Krejčiřík and Pratelli (Pac J Math 254(2):309–333, 2011), 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.

Authors with CRIS profile

Aldo Pratelli Lehrstuhl für Analysis

Involved external institutions

Università degli Studi di Modena e Reggio Emilia (UNIMORE) IT Italy (IT)

How to cite

APA:

Leonardi, G.P., & Pratelli, A. (2016). On the Cheeger sets in strips and non-convex domains. Calculus of Variations and Partial Differential Equations, 55(1), 1-28. https://dx.doi.org/10.1007/s00526-016-0953-3

MLA:

Leonardi, Gian Paolo, and Aldo Pratelli. "On the Cheeger sets in strips and non-convex domains." Calculus of Variations and Partial Differential Equations 55.1 (2016): 1-28.

BibTeX: Download