Characterization of gradient young measures generated by homeomorphisms in the plane
Characterization of gradient young measures generated by homeomorphisms in the plane
复制标题
平面同胚产生的梯度年轻测度的表征
DOI：
10.1051/cocv/2015003
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. Kružík
中科院分区：
文献类型：
--
作者：
B. Benesová;M. Kružík
我们刻画了平面上双Lipschitz保向映射的梯度生成的Young测度。这个问题的动机是变分问题的非线性弹性的方向保持和可容许的变形的内射性是关键的要求。这些结果使我们能够得到新的弱下连续性结果的积分泛函依赖于梯度。作为应用，我们证明了在双Lipschitz同胚中具有非多凸能量密度的积分泛函的极小元的存在性。
We characterize Young measures generated by gradients of bi-Lipschitz orientation-preserving maps in the plane. This question is motivated by variational problems in nonlinear elasticity where the orientation preservation and injectivity of the admissible deformations are key requirements. These results enable us to derive new weak∗ lower semicontinuity results for integral functionals depending on gradients. As an application, we show the existence of a minimizer for an integral functional with nonpolyconvex energy density among bi-Lipschitz homeomorphisms.