کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4589683 1334897 2016 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
L∞ estimates in optimal mass transportation
ترجمه فارسی عنوان
لا ؟؟ برآورد در حمل و نقل جرم مطلوب
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We show that in any complete metric space the probability measures μ with compact and connected support are the ones having the property that the optimal transportation distance to any other probability measure ν living on the support of μ   is bounded below by a positive function of the L∞L∞ transportation distance between μ and ν. The function giving the lower bound depends only on the lower bound of the μ-measures of balls centered at the support of μ and on the cost function used in the optimal transport. We obtain an essentially sharp form of this function.In the case of strictly convex cost functions we show that a similar estimate holds on the level of optimal transport plans if and only if the support of μ is compact and sufficiently close to being a geodesic metric space in the quantitative sense that between any two points there exists a sequence along which the cost can be cyclically decreased.We also study when convergence of compactly supported measures in LpLp transportation distance implies convergence in L∞L∞ transportation distance. For measures with connected supports this property is characterized by uniform lower bounds on the measures of balls centered at the supports of the measures or, equivalently, by the Hausdorff-convergence of the supports.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 270, Issue 11, 1 June 2016, Pages 4297–4321
نویسندگان
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