Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

S. Dipierro - F. Onoue - E. Valdinoci

(Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property

created by onoue on 09 Oct 2020

[BibTeX]

Submitted Paper

Inserted: 9 oct 2020

Pages: 13
Year: 2020

ArXiv: 2010.00798 PDF

Abstract:

We consider nonlocal minimal surfaces in a cylinder with prescribed datum given by the complement of a slab. We show that when the width of the slab is large the minimizers are disconnected and when the width of the slab is small the minimizers are connected. This feature is in agreement with the classical case of the minimal surfaces. Nevertheless, we show that when the width of the slab is large the minimizers are not flat discs, as it happens in the classical setting, and, in particular, in dimension 2 we provide a quantitative bound on the stickiness property exhibited by the minimizers. Moreover, differently from the classical case, we show that when the width of the slab is small then the minimizers completely adhere to the side of the cylinder, thus providing a further example of stickiness phenomenon.

Credits | Cookie policy | HTML 5 | CSS 2.1