Global invertibility of Sobolev maps

被引：8
|
作者：
Henao, Duvan [2 ]
Mora-Corral, Carlos [1 ]
Oliva, Marcos [3 ]
机构：
[1] Univ Autonoma Madrid, Dept Math, Madrid, Spain
[2] Pontificia Univ Catolica Chile, Fac Matemat, Santiago, Chile
[3] PiperLab, Madrid, Spain
来源：
ADVANCES IN CALCULUS OF VARIATIONS | 2021年 / 14卷 / 02期
关键词：
Global invertibility; Sobolev maps; nonlinear elasticity;
D O I：
10.1515/acv-2018-0053
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We define a class of Sobolev W1-p(Omega, R-n) functions, with p > n -1, such that its trace on de is also Sobolev, and do not present cavitation in the interior or on the boundary. We show that if a function in this class has positive Jacobian and coincides on the boundary with an injective map, then the function is itself injective. We then prove the existence of minimizers within this class for the type of functionals that appear in nonlinear elasticity.
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页码：207 / 230
页数：24
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