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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U.S. is partially supported by FP7-IDEAS-ERC-StG Grant #200497 (BioSMA).
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Spadaro, E., Stefanelli, U. A variational view at the time-dependent minimal surface equation. J. Evol. Equ. 11, 793–809 (2011). https://doi.org/10.1007/s00028-011-0111-5
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DOI: https://doi.org/10.1007/s00028-011-0111-5