کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4604274 | 1337429 | 2014 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Counterexample to regularity in average-distance problem
ترجمه فارسی عنوان
مثلا به طور منظم در مسافت متوسط فاصله
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
The average-distance problem is to find the best way to approximate (or represent) a given measure μ on Rd by a one-dimensional object. In the penalized form the problem can be stated as follows: given a finite, compactly supported, positive Borel measure μ, minimizeE(Σ)=â«Rdd(x,Σ)dμ(x)+λH1(Σ) among connected closed sets, Σ, where λ>0, d(x,Σ) is the distance from x to the set Σ, and H1 is the one-dimensional Hausdorff measure. Here we provide, for any d⩾2, an example of a measure μ with smooth density, and convex, compact support, such that the global minimizer of the functional is a rectifiable curve which is not C1. We also provide a similar example for the constrained form of the average-distance problem.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 31, Issue 1, JanuaryâFebruary 2014, Pages 169-184
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 31, Issue 1, JanuaryâFebruary 2014, Pages 169-184
نویسندگان
Dejan SlepÄev,