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A measure theoretic approach to higher codimension mean curvature flows. (English) Zbl 1043.35136
Summary: We develop a generalization of the theory of varifolds and use it in the asymptotic study of a sequence of Ginzburg-Landau systems. These equations are reaction-diffusion type, nonlinear partial differential equations, and the main object of our study is the renormalized energy related to these systems. Under suitable density assumptions, we show convergence to a Brakke flow by mean curvature. The proof is based on a suitable generalization of the theory of varifolds and on the analysis of the gradient Young measures associated to the solutions of the system.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35K55 Nonlinear parabolic equations
49Q20 Variational problems in a geometric measure-theoretic setting
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