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Session 23. Nonlinear Evolution Equations and their Applications
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Variational analysis of a reduced Allen-Cahn action functional |
Matthias Röger, Technische Universität Dortmund, Germany
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The talk is based on the joint work with Annibale Magni (Münster)
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We consider the sharp interface limit of the Allen-Cahn action
functional. For suitable evolutions of (generalized) hypersurfaces
this functional consists of the sum of the squares of the mean
curvature and of the velocity vectors, integrated over time and
space. Given initial and final conditions we investigate the
corresponding action minimization problem. We propose a generalized
formulation, prove compactness and lower-semicontinuity properties
and characterize the Euler-Lagrange and conserved quantities.
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