On the Cheeger sets in strips and non-convex domains

Journal article
(Original article)


Publication Details

Author(s): Leonardi GP, Pratelli A
Journal: Calculus of Variations and Partial Differential Equations
Publisher: Springer Verlag (Germany)
Publication year: 2016
Volume: 55
Journal issue: 1
Pages range: 1-28
ISSN: 0944-2669


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.



FAU Authors / FAU Editors

Pratelli, Aldo Prof.
Lehrstuhl für Mathematik


External institutions with authors

Università degli Studi di Modena e Reggio Emilia (UNIMORE)


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: 

Last updated on 2018-17-10 at 16:10