The goal of this note is to identify the minimal number of linear forms which is necessary to obtain some inequalities of Korn's type. In other words we give some results allowing to estimate the $L^2$-norm of the gradient of a vector field in terms of a minimal sum of $L^2$-norms of linear forms of this gradient. We consider such inequalities either over ${\mathbb{H}}_0^1(\mathrm{\Omega })$ or ${\mathbb{H}}^1(\mathrm{\Omega })$.

中文翻译：

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关于康恩类型的不等式

本注释的目的是确定最小数量的线性形式，这对于获得Korn类型的某些不等式是必需的。换句话说，我们给出了一些结果，可以估算${\mathrm{大号}}^{\mathrm{2个}}$向量场梯度的最小范数 ${\mathrm{大号}}^{\mathrm{2个}}$-此梯度的线性形式的范数。我们认为这种不平等是${\mathbb{H}}_0^{\mathrm{1个}}（\mathrm{\Omega }）$ 或者 ${\mathbb{H}}^{\mathrm{1个}}（\mathrm{\Omega }）$。