Title:	On the Cheeger problem for rotationally invariant domains domains
Authors:	Bobkov, Vladimír Parini, Enea
Citation:	BOBKOV, V. PARINI, E. On the Cheeger problem for rotationally invariant domains domains. MANUSCRIPTA MATHEMATICA, 2021, roč. 166, č. 3-4, s. 503-522. ISSN: 0025-2611
Issue Date:	2021
Publisher:	Springer
Document type:	článek article
URI:	2-s2.0-85095999523 http://hdl.handle.net/11025/47286
ISSN:	0025-2611
Keywords in different language:	Cheeger problem;rotationally invariant domains
Abstract in different language:	We investigate the properties of the Cheeger sets of rotationally invariant, bounded domains ⊂ Rn. For a rotationally invariant Cheeger set C, the free boundary ∂C ∩ consists of pieces of Delaunay surfaces, which are rotationally invariant surfaces of constant mean curvature. We show that if is convex, then the free boundary of C consists only of pieces of spheres and nodoids. This result remains valid for nonconvex domains when the generating curve of C is closed, convex, and of class C1,1. Moreover, we provide numerical evidence of the fact that, for general nonconvex domains, pieces of unduloids or cylinders can also appear in the free boundary of C.
Rights:	© Springer
Appears in Collections:	OBD

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