SOME NOTES ON FUNCTIONS OF LEAST W3,1 -FRACTIONAL SEMINORM

被引：0
|
作者：
Bucur, Claudia [1 ]
机构：
[1] Dip Matemat Federigo Enriques, Via Saldini 50, I-20133 Milan, Italy
来源：
BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR | 2023年 / 14卷 / 01期
关键词：
Fractional; 1-Laplacian; nonlocal operators; nonlocal minimal surfaces; IMAGE DECOMPOSITION; GRADIENT;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this survey we discuss some existence and asymptotic results, originally obtained in [4, 3], for functions of least W-8,W-1-fractional seminorm. We present the con-nection between these functions and nonlocal minimal surfaces, leveraging this relation to build a function of least fractional seminorm. We further prove that a function of least fractional seminorm is the limit for p ? 1 of the sequence of minimizers of the W8,p-energy. Additionally, we consider the fractional 1-Laplace operator and study the equivalence between weak solutions and functions of least fractional seminorm.
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页码：38 / 57
页数：20
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