Report
A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I
| العنوان: | A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I |
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| المؤلفون: | Comi, Giovanni E., Stefani, G. |
| المصدر: | Rev. Mat. Complut. 36, 491-569 (2023) |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, 26A33, 26B30, 28A33 |
| الوصف: | We continue the study of the space $BV^\alpha(\mathbb{R}^n)$ of functions with bounded fractional variation in $\mathbb{R}^n$ of order $\alpha\in(0,1)$ introduced in arXiv:1809.08575, by dealing with the asymptotic behaviour of the fractional operators involved. After some technical improvements of certain results of our previous work, we prove that the fractional $\alpha$-variation converges to the standard De Giorgi's variation both pointwise and in the $\Gamma$-limit sense as $\alpha\to1^-$. We also prove that the fractional $\beta$-variation converges to the fractional $\alpha$-variation both pointwise and in the $\Gamma$-limit sense as $\beta\to\alpha^-$ for any given $\alpha\in(0,1)$. Comment: 61 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s13163-022-00429-y |
| URL الوصول: | http://arxiv.org/abs/1910.13419 |
| رقم الانضمام: | edsarx.1910.13419 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s13163-022-00429-y |
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