The trace-dev-div inequality in $H^s$ controls the trace in the norm of $H^s$ by that of the deviatoric part plus the $H^{s-1}$ norm of the divergence of a quadratic tensor field different from the constant unit matrix. This is well known for $s=0$ and established for orders $0\le s\le 1$ and arbitrary space dimension in this note. For mixed and least-squares finite element error analysis in linear elasticity, this inequality allows to establish robustness with respect to the Lam\'e parameter $\lambda$.

翻译：$H^s$ 空间中的迹-偏差-散度不等式通过偏差部分及与常数单位矩阵不同的二阶张量场的 $H^{s-1}$ 范数散度，来控制迹在 $H^s$ 范数下的值。该不等式在 $s=0$ 时已熟知，本文针对任意空间维度建立了 $0\le s\le 1$ 阶的结果。在线弹性混合元与最小二乘有限元误差分析中，该不等式可确保关于拉梅参数 $\lambda$ 的鲁棒性。