کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4589660 1334895 2016 39 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Metric selfduality and monotone vector fields on manifolds
ترجمه فارسی عنوان
خودآلویزی متریک و رشتههای بردار منحصر به فرد در منیفولد
کلمات کلیدی
حمل و نقل جرم مطلوب، نقشه های مونوتونی در منیفولد، اصول اختیاری
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We develop a “metrically selfdual” variational calculus for c-monotone vector fields between general manifolds X and Y, where c   is a coupling on X×YX×Y. Remarkably, many of the key properties of classical monotone operators known to hold in a linear context extend to this non-linear setting. This includes an integral representation of c-monotone vector fields in terms of c-convex selfdual Lagrangians, their characterization as a partial c-gradients of antisymmetric Hamiltonians, as well as the property that these vector fields are generically single-valued. We also use a symmetric Monge–Kantorovich transport to associate to any measurable map its closest possible c-monotone “rearrangement”. We also explore how this metrically selfdual representation can lead to a global variational approach to the problem of inverting c-monotone maps, an approach that has proved efficient for resolving non-linear equations and evolutions driven by monotone vector fields in a Hilbertian setting.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 271, Issue 6, 15 September 2016, Pages 1652–1690
نویسندگان
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