Compactness of Special Functions of Bounded Higher Variation

• Autorzy: Luigi Ambrosio , Francesco Ghiraldin
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Higher codimension singularities; nonlinear elasticity; geometric measure theory; distributional jacobian; flat currents; special bounded variation; compactness; bounded higher variation; Mumford-Shah; free discountinuity

Kategorie tematyczne

• 49Q20: Variational problems in a geometric measure-theoretic setting
• 49J45: Methods involving semicontinuity and convergence; relaxation
• 49Q15: Geometric measure and integration theory, integral and normal currents

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2013
• Tom: 1
• Strony: 1-30

Daty

otrzymano

2012-10-16

zaakceptowano

2012-12-07

online

2013-01-04

Twórcy

autor

Luigi Ambrosio

• Scuola Normale Superiore di Pisa,
  Piazza dei Cavalieri 7, I-56126, Pisa, Italy

autor

Francesco Ghiraldin

• Scuola Normale Superiore di Pisa,
  Piazza dei Cavalieri 7, I-56126, Pisa, Italy

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Identyfikatory

DOI

10.2478/agms-2012-0001