LOWER SEMICONTINUITY IN BV OF QUASICONVEX INTEGRALS WITH SUBQUADRATIC GROWTH

被引：4
|
作者：
Soneji, Parth [1 ]
机构：
[1] Univ Oxford, Inst Math, Oxford OX1 3LB, England
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2013年 / 19卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
Lower semicontinuity; quasiconvex integrals; functions of bounded variation; MULTIPLE INTEGRALS; RELAXATION; DEFINITION;
D O I：
10.1051/cocv/2012021
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A lower semicontinuity result in BV is obtained for quasiconvex integrals with subquadratic growth. The key steps in this proof involve obtaining boundedness properties for an extension operator, and a precise blow-up technique that uses fine properties of Sobolev maps. A similar result is obtained by Kristensen in [Calc. Var. Partial Differ. Equ. 7 (1998) 249-261], where there are weaker asssumptions on convergence but the integral needs to satisfy a stronger growth condition.
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页码：555 / 573
页数：19
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