Geodesic
Compactness of Special Functions of Bounded Higher Variation
Analysis and Geometry in Metric Spaces, Tome 1 (2013) no. 1, pp. 1-30.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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 [43] and the corresponding SBnV space studied by De Lellis in [24]. In this class of spaces, which allow as in [43] 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].
Mots-clés : Higher codimension singularities, nonlinear elasticity, geometric measure theory, distributional jacobian, flat currents, special bounded variation, compactness, bounded higher variation, Mumford-Shah, free discountinuity 
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Ambrosio, Luigi; Ghiraldin, Francesco. Compactness of Special Functions of Bounded Higher Variation. Analysis and Geometry in Metric Spaces, Tome 1 (2013) no. 1, pp. 1-30. http://geodesic.mathdoc.fr/item/AGMS_2013_1_1_a0/