Exterior convexity and classical calculus of variations
Exterior convexity and classical calculus of variations
复制标题
外凸性和经典变分法
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Swarnendu Sil
中科院分区：
文献类型：
--
作者：
S. Bandyopadhyay;Swarnendu Sil
我们研究[S. Bandyopadhyay，B. Dacorogna 和 S. Sil，J. Eur。数学。苏克。 17 (2015) 1009–1039.] 具有一级凸性、拟凸性和多凸性的经典概念。为此，我们引入了投影图，它以一种新的方式推广了两个张量的交替投影，并研究了该图的代数性质。我们以这种关系的一些简单推论作为结论，这为 [S. Bandyopadhyay，B. Dacorogna 和 S. Sil，J. Eur。数学。苏克。 17（2015）1009–1039。]。
We study the relation between various notions of exterior convexity introduced in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009–1039.] with the classical notions of rank one convexity, quasiconvexity and polyconvexity. To this end, we introduce a projection map, which generalizes the alternating projection for two-tensors in a new way and study the algebraic properties of this map. We conclude with a few simple consequences of this relation which yields new proofs for some of the results discussed in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009–1039.].