کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4615160 | 1339309 | 2015 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Sup–Inf explicit formulas for minimal Lipschitz extensions for 1-fields on RnRn
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We study the relationship between the Lipschitz constant of 1-field introduced in [12] and the Lipschitz constant of the gradient canonically associated with this 1-field. Moreover, we produce two explicit formulas which are two extremal minimal Lipschitz extensions for 1-fields. As a consequence of the previous results, for the problem of minimal extension by Lipschitz continuous functions from RmRm to RnRn, we produce explicit formulas similar to those of Bauschke and Wang (see [7]). Finally, we show that Wells's extensions (see [24]) of 1-fields are absolutely minimal Lipschitz extensions when the domain of 1-field to expand is finite. We provide a counter-example showing that this result is false in general.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 424, Issue 2, 15 April 2015, Pages 1161–1185
Journal: Journal of Mathematical Analysis and Applications - Volume 424, Issue 2, 15 April 2015, Pages 1161–1185
نویسندگان
Erwan Y. Le Gruyer, Thanh Viet Phan,