We study a class of non smooth vector valued maps, defined on n-dimensional domains, which allow for fractures of any integer dimension lower than n.We extend some well known features about (n−1)-dimensional jumps ofSBV functions and 0-dimensional singularities, or cavitations, of the distributional determinant of Sobolev functions. Variational problems involving the size of the fractures of any dimension are then studied.
Fractures and vector valued maps / Mucci, Domenico. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 22:4(2005), pp. 391-420. [10.1007/s00526-004-0282-9]
Fractures and vector valued maps
MUCCI, Domenico
2005
Abstract
We study a class of non smooth vector valued maps, defined on n-dimensional domains, which allow for fractures of any integer dimension lower than n.We extend some well known features about (n−1)-dimensional jumps ofSBV functions and 0-dimensional singularities, or cavitations, of the distributional determinant of Sobolev functions. Variational problems involving the size of the fractures of any dimension are then studied.
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