In:
Advanced Nonlinear Studies, Walter de Gruyter GmbH, Vol. 19, No. 1 ( 2019-02-01), p. 55-68
Abstract:
The paper is related to a conjecture by Pegon, Santambrogio and Xia concerning the dimension of the boundary of some sets which we are calling “irrigation balls”. We propose a notion of sub-balls and sub-spheres of prescribed radius and we prove that, generically, the only possible Minkowski dimension of sub-spheres is the one expected in the conjecture. At the same time, beside the scale transition properties and the dimension estimates on some significant sets, we propose a third approach to study the fractal regularity which relies on lower oscillation estimates on the landscape function, which turns out to behave as a Weierstrass-type function.
Type of Medium:
Online Resource
ISSN:
1536-1365
,
2169-0375
DOI:
10.1515/ans-2018-2035
Language:
English
Publisher:
Walter de Gruyter GmbH
Publication Date:
2019
detail.hit.zdb_id:
2482156-1
SSG:
17,1
Bookmarklink