This article is divided into two parts. In the first part we show that a set E has locally finite s-perimeter if and only if it can be approximated in an appropriate sense by smooth open sets. In the second part we prove some elementary properties of local and global s-minimal sets, such as existence and compactness. We also compare the two notions of minimizer (i.e., local and global), showing that in bounded open sets with Lipschitz boundary they coincide. Conversely, in general this is not true in unbounded open sets, where a global s-minimal set may fail to exist (we provide an example in the case of a cylinder Omega x R).
Approximation of sets of finite fractional perimeter by smooth sets and comparison of local and global $s$-minimal surfaces / L. Lombardini. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - 20:2(2018), pp. 261-296.
|Titolo:||Approximation of sets of finite fractional perimeter by smooth sets and comparison of local and global $s$-minimal surfaces|
LOMBARDINI, LUCA (Primo) (Corresponding)
|Parole Chiave:||nonlocal minimal surfaces; smooth approximation; existence theory; subgraphs|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4171/IFB/402|
|Appare nelle tipologie:||01 - Articolo su periodico|