Fractures and vector valued maps

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 of SBV 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.Received: 10 September 2003, Accepted: 5 April 2004, Published online: 16 July 2004Mathematics Subject Classification (2000): 49Q15, 28A75, 49J52