Titlebook: Local Minimization, Variational Evolution and Γ-Convergence; Andrea Braides Book 2014 Springer International Publishing Switzerland 2014 4

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Convergence of Local Minimizers,duce the existence and convergence of local minimizers of the converging sequence. This version of the fundamental theorem of .-convergence can be coupled with scaling arguments, which may give existence of multiple local minimizers, and in some cases a density result. This approach to showing exist

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Minimizing Movements,to the study of local minimizers, which provide stationary solutions for such motions, and is a way of defining a gradient flow for smooth energies, but is defined for a wide class of (non-smooth) energies. For the sake of simplicity of exposition, we limit our analysis to a Hilbert setting, even th

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Minimizing Movements Along a Sequence of Functionals,time scale . and the parameter . in the energies. In general, the final evolution depends on the .-. regime. The extreme case are the minimizing movements for the .-limit . (for “fast-converging .”) and the limits of minimizing movements for . as . (for “fast-converging .”). Heuristically, minimizin

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Different Time Scales,d study long-time behaviour of variational motions, such as the ones connected to Mumford–Shah or Perona–Malik energies, Lennard-Jones discrete systems, or the gradient theory of phase transitions. These are obtained by suitably choosing a diverging (but positive) scaling of the energies. Negative s

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Stability Theorems, to . with initial data . converging to . .. In Sect.. it is proved that by suitably choosing . the minimizing movement along the sequence . from . converges to a minimizing movement for the limit . from . .. A further issue is whether, by assuming some further properties on . we may deduce that the

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zu verfassen, habe ich sie ohne zu zö­ gern und mit Freude, mit Ja beantwortet. Ich hatte nämlich an­ genommen, daß ich aufgrund meiner verhältnismäßig langen Tätig­ keit auf einer Intensivstation mit einem gemischten Patienten­ kollektiv unter der Leitung von Professor R. Kucher und später von Pro

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