The L1-relaxed area of the graph of the vortex map: Optimal lower bound

被引：0
|
作者：
Bellettini, Giovanni [1 ,2 ]
Elshorbagy, Alaa [3 ]
Scala, Riccardo [1 ]
机构：
[1] Univ Siena, Dipartimento Ingn Informaz & Sci Matemat, I-53100 Siena, Italy
[2] Abdus Salaam Int Ctr Theoret Phys, Math Sect, I-34151 Trieste, Italy
[3] Tech Univ Dortmund, Fak Math, D-44227 Dortmund, Germany
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2025年 / 256卷
关键词：
Relaxation; Cartesian currents; Area functional; Minimal surfaces; Plateau problem; LOWER SEMICONTINUITY; PLANE;
D O I：
10.1016/j.na.2025.113803
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a lower bound for the value of the L1-relaxed area of the graph of the map u:Bl(0)\{0}subset of R-2 -> R-2, u(x):=x/|x|, x not equal 0, for all values of the radius l>0. In the computation of the singular part of the relaxed area, for l in a certain range, in particular l not too large, a nonparametric Plateau-type problem with partial free boundary has to be solved. Our lower bound turns out to be optimal, in view of an upper bound proven in a companion paper
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页数：47
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