Topological singular set for vector-valued maps and applications
speaker: Giandomenico Orlandi (Università di Verona )abstract: We introduce an operator S on vector-valued maps u which has the ability to capture the relevant topological information carried by u. In particular, this operator is defined on maps that take values in a closed submanifold N of the Euclidean space Rm, and coincides with the distributional Jacobian in case N is a sphere. More precisely, the range of S is a set of maps whose values are flat chains with coefficients in a suitable normed abelian group. We use S to characterise strong limits of smooth N -valued maps with respect to Sobolev norms, extending a result by Pakzad and Riviere. Moreover, we apply it to the study of the asymptotic behaviour of minimisers of Ginzburg-Landau type functionals arising in materials science. This is joint work with G. Canevari (Verona).
timetable:
Mon 6 Sep, 16:10 - 17:00, Aula Dini
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