On symmetric div-quasiconvex hulls and divsym-free $\mathrm{L}^\infty$-truncations
| Autor: | Behn, Linus, Gmeineder, Franz, Schiffer, Stefan |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We establish that for any non-empty, compact set $K\subset\mathbb{R}_{\mathrm{sym}}^{3\times 3}$ the $1$- and $\infty$-symmetric div-quasiconvex hulls $K^{(1)}$ and $K^{(\infty)}$ coincide. This settles a conjecture in a recent work of Conti, M\"{u}ller and Ortiz (Symmetric Div-Quasiconvexity and the Relaxation of Static Problems. Arch. Ration. Mech. Anal. 235(2):841-880) in the affirmative. As a key novelty, we construct an $\mathrm{L}^{\infty}$-truncation that preserves both symmetry and solenoidality of matrix-valued maps in $\mathrm{L}^{1}$. Comment: 35 pages, 1 figure |
| Databáze: | arXiv |
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