Given an open set Ω ⊂ Rm and n > 1, we introduce the new spaces GBnV(Ω) of Generalized functions of bounded higher variation and GSBnV(Ω) of Generalized special functions of bounded higher variation that generalize, respectively, the space BnV introduced by Jerrard and Soner in  and the corresponding SBnV space studied by De Lellis in . In this class of spaces, which allow as in  the description of singularities of codimension n, the distributional jacobian Ju need not have finite mass: Roughly speaking, finiteness of mass is not required for the (m - n)-dimensional part of Ju, but only finiteness of size. In the space GSBnV we are able to provide compactness of sublevel sets and lower semicontinuity of Mumford-Shah type functionals, in the same spirit of the codimension 1 theory [5, 6].
|Titolo:||Compactness of special functions of bounded higher variation|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.2478/agms-2012-0001|
|Appare nelle tipologie:||1.1 Articolo in rivista|