A characterization of the total variation TV of the Jacobian determinant detDu is obtained for some classes of functions u in R^n outside the traditional regularity space W^(1,n). In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity. Relations between TV and the distributional determinant DetDu are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals.
Topological Degree, Jacobian Determinants and Relaxation / I. FONSECA.; N. FUSCO; P. MARCELLINI. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. A. - ISSN 0392-4033. - STAMPA. - 8:(2005), pp. 187-250.
Topological Degree, Jacobian Determinants and Relaxation
MARCELLINI, PAOLO
2005
Abstract
A characterization of the total variation TV of the Jacobian determinant detDu is obtained for some classes of functions u in R^n outside the traditional regularity space W^(1,n). In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity. Relations between TV and the distributional determinant DetDu are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals.
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