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- W4382723477 abstract "We characterise all linear maps $mathcal{A}colonmathbb{R}^{ntimes n}tomathbb{R}^{ntimes n}$ such that, for $1leq p<n$, begin{align*} |P|_{L^{p^{*}}(mathbb{R}^{n})}leq c,Big(|mathcal{A}[P]|_{L^{p^{*}}(mathbb{R}^{n})}+|mathrm{Curl} P|_{L^{p}(mathbb{R}^{n})} Big) end{align*} holds for all compactly supported $Pin C_{c}^{infty}(mathbb{R}^{n};mathbb{R}^{ntimes n})$, where $mathrm{Curl} P$ displays the matrix curl. Being applicable to incompatible, that is, non-gradient matrix fields as well, such inequalities generalise the usual Korn-type inequalities used e.g. in linear elasticity. Different from previous contributions, the results gathered in this paper are applicable to all dimensions and optimal. This particularly necessitates the distinction of different constellations between the ellipticities of $mathcal{A}$, the integrability $p$ and the underlying space dimensions $n$, especially requiring a finer analysis in the two-dimensional situation." @default.
- W4382723477 created "2023-07-01" @default.
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- W4382723477 date "2023-06-29" @default.
- W4382723477 modified "2023-09-26" @default.
- W4382723477 title "Optimal incompatible Korn–Maxwell–Sobolev inequalities in all dimensions" @default.
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- W4382723477 doi "https://doi.org/10.1007/s00526-023-02522-6" @default.
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