A variational view at the time-dependent minimal surface equation |
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Authors: | Emanuele Spadaro Ulisse Stefanelli |
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Institution: | 1. Hausdorff Center for Mathematics, Endenicher Allee 60, D-53115, Bonn, Germany 2. IMATI?CCNR, v. Ferrata 1, I-27100, Pavia, Italy
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Abstract: | We present a global variational approach to the L
2-gradient flow of the area functional of cartesian surfaces through the study of the so-called weighted energy-dissipation (WED) functional. In particular, we prove a relaxation result which allows us to show that minimizers of the WED converge
in a quantitatively prescribed way to gradient-flow trajectories of the relaxed area functional. The result is then extended
to general parabolic quasilinear equations arising as gradient flows of convex functionals with linear growth. |
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Keywords: | |
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