We establish the first partial regularity results for (strongly) symmetric quasiconvex functionals of linear growth on BD, the space of functions of bounded deformation. By Rindler's foundational work [64], symmetric quasiconvexity is the pivotal notion as regards sequential weak*-lower semicontinuity and hence for the existence of minima of the relaxed functionals on BD. The overarching main difficulty here is the lack of Korn's Inequality in the ${\mathrm{L}}^1$-setting, hereby implying that the BD-case is genuinely different from the study of variational integrals on BV. Unlike for superlinear growth, symmetric quasiconvex functionals, where we establish partial regularity by direct reduction to the full gradient case by Korn-type inequalities, such a reduction does not work in the linear growth case and identifies the latter as the only situation requiring a treatment on its own.

我们为BD上线性增长的（强烈）对称拟凸函数（有限变形函数的空间）建立了第一部分正则性结果。根据Rindler的基础工作[64]，对称拟凸性是关于连续弱*-下半连续性的关键概念，因此对于BD上松弛函数的最小值存在。这里最主要的主要困难是缺乏Korn的不等式。${\mathrm{大号}}^{\mathrm{1个}}$设置，因此暗示BD情况与BV的变分积分研究确实不同。与超线性增长的对称拟凸函数不同，在这种情况下，我们通过利用Korn型不等式直接还原为全梯度情况来建立部分正则性，这种减少不适用于线性增长情况，并将后者确定为唯一需要处理的情况在其自己的。