Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints

被引：22

作者：

Arroyo-Rabasa, Adolfo ^{[1
]}

De Philippis, Guido ^{[2
]}

Rindler, Filip ^{[3
]}

机构：

[1] Univ Leipzig, Math Inst, Augustuspl 10, D-04109 Leipzig, Germany

[2] Scuola Int Super Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy

[3] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

来源：

ADVANCES IN CALCULUS OF VARIATIONS | 2020年 / 13卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Lower semicontinuity; functional on measures; A-quasiconvexity; generalized Young measure; A-QUASICONVEXITY; YOUNG MEASURES; CONVEX; BV;

D O I：

10.1515/acv-2017-0003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary order). These results generalize several known lower semicontinuity and relaxation theorems for BV, BD, and for more general first-order linear PDE side constrains. Our proofs are based on recent progress in the understanding of singularities of measure solutions to linear PDEs and of the generalized convexity notions corresponding to these PDE constraints.

引用

页码：219 / 255

页数：37

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