ORIENTATION-PRESERVING YOUNG MEASURES
ORIENTATION-PRESERVING YOUNG MEASURES
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保持青少年定向的措施
DOI：
10.1093/qmath/haw019
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Koumatos K
中科院分区：
文献类型：
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作者：
Koumatos K
我们证明了一个特征的精神Kinderlehrer-Pedregal定理的Sobolev映射满足方向保持约束的梯度所产生的Young措施，即点态雅可比矩阵是积极的几乎无处不在。的论点，以构建适当的生成序列，从这样的杨措施是基于一个变体的凸整合结合一个明确的分层结构在矩阵空间。我们的生成序列是有界的inforless比空间维度，一个政权中的点态雅可比矩阵的行为灵活，我们的结果所示。另一方面，对于大于或等于空间维度的情况必然变得僵化，这里所提出的构造不可能成功。给出了在Sobolev空间中积分泛函的松弛、保向壳理论和弱保向映射用严格保向映射逼近等方面的应用。
We prove a characterization result in the spirit of the Kinderlehrer–Pedregal Theorem for Young measures generated by gradients of Sobolev maps satisfying the orientation-preserving constraint, that is, the pointwise Jacobian is positive almost everywhere. The argument to construct the appropriate generating sequences from such Young measures is based on a variant of convex integration in conjunction with an explicit lamination construction in matrix space. Our generating sequence is bounded inforless than the space dimension, a regime in which the pointwise Jacobian behaves flexibly, as is illustrated by our results. On the other hand, forlarger than or equal to the space dimension the situation necessarily becomes rigid and a construction as presented here cannot succeed. Applications to relaxation of integral functionals, the theory of semiconvex hulls and approximation of weakly orientation-preserving maps by strictly orientation-preserving ones in Sobolev spaces are given.