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楼主: cucumber
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Convex Functionals in ,(,) will discuss in detail in 9.3.1, 9.3.4, 9.3.6. His original motivation was to prove the uniqueness of the minimizer of an energy functional which results from the sum of the above three contributions.
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Metric Slope and Subdifferential Calculus in ,(,)ed in a Hilbert space ., the . : . → 2. of . is a multivalued operator defined as . which we will also write in the equivalent form for . ∈ .(.) . As usual in multivalued analysis, the proper domain .(.) ⊂ .(.) is defined as the set of all . ∈ . such that .(.) ≠ φ; we will use this convention for al
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Distribution of Media and Informationderivative of an absolutely continuous curve with values in . and the upper gradients of a functional defined in .. The related definitions are presented in the next two sections (a more detailed treatment of this topic can be found for instance in [20]); the last one deals with curves of maximal sl
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Introduction: New Food Politics,ity estimates are then derived for discrete solutions which yield Proposition 2.2.3 by a compactness argument. Finally, convergence is obtained by combining the a priori energy estimates with the gradient properties of the relaxed slope. We will conclude this section with the proof of Theorem 2.4.15
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Johannes Pause,Niels-Oliver Walkowskigy . with the “strong” one induced by the distance . as in Remark 2.1.1: thus we are assuming that . but .. Existence, uniqueness and semigroup properties for minimizing movement . ∈ .(Φ; .) (and not simply the generalized ones, recall Definition 2.0.6) are well known in the case of lower semicontin
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