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Compactness of Special Functions of Bounded Higher Variation

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Ambrosio L., Ghiraldin F.

Analysis and Geometry in Metric Spaces

2013

tom 1

1-30

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].

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Ambrosio L.

1 Ghiraldin F.

1 2013

Wyniki wyszukiwania

Compactness of Special Functions of Bounded Higher Variation