تقرير
Continuity of s-minimal functions
| العنوان: | Continuity of s-minimal functions |
|---|---|
| المؤلفون: | Bucur, Claudia, Dipierro, Serena, Lombardini, Luca, Valdinoci, Enrico |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs |
| الوصف: | We consider the minimization property of a Gagliardo-Slobodeckij seminorm which can be seen as the fractional counterpart of the classical problem of functions of least gradient and which is related to the minimization of the nonlocal perimeter functional. We discuss continuity properties for this kind of problem. In particular, we show that, under natural structural assumptions, the minimizers are bounded and continuous in the interior of the ambient domain (and, in fact, also continuous up to the boundary under some mild additional hypothesis). We show that these results are also essentially optimal, since in general the minimizer is not necessarily continuous across the boundary. Comment: 15 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.20079 |
| رقم الأكسشن: | edsarx.2407.20079 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |