We investigate uniqueness issues for a continuity equation arising out of the simplest model for plasticity, Hencky plasticity. The associated system is of the form $\mathit{curl}\left(\mathit{\mu \sigma }\right)=0$ where 𝜇 is a nonnegative measure and 𝜎 a two-dimensional divergence-free unit vector field. After establishing the Sobolev regularity of that field, we provide a precise description of all possible geometries of the characteristic flow, as well as of the associated solutions. © 2022 Courant Institute of Mathematics and Wiley Periodicals LLC.

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标量 Hencky 塑性的连续性方程和特征流

我们研究由最简单的塑性模型 Hencky 塑性产生的连续性方程的唯一性问题。关联系统的形式为$\mathit{卷曲}\left(\mathit{\mu \sigma }\right)=0$其中 𝜇 是非负测度，𝜎 是二维无散度单位向量场。在建立该场的索博列夫正则性之后，我们提供了特征流的所有可能几何形状以及相关解决方案的精确描述。© 2022 Courant 数学研究所和 Wiley periodicals LLC。