On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations
Behn L, Gmeineder F, Schiffer S (2021)
arXiv:2108.05757.
Preprint | Englisch
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Autor*in
Behn, LinusUniBi 
;
Gmeineder, Franz;
Schiffer, Stefan
;
Gmeineder, Franz;
Schiffer, StefanEinrichtung
Abstract / Bemerkung
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 $\mathrm{L}^{1}$.
Erscheinungsjahr
2021
Zeitschriftentitel
arXiv:2108.05757
Page URI
https://pub.uni-bielefeld.de/record/2960500
Zitieren
Behn L, Gmeineder F, Schiffer S. On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations. arXiv:2108.05757. 2021.
Behn, L., Gmeineder, F., & Schiffer, S. (2021). On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations. arXiv:2108.05757
Behn, Linus, Gmeineder, Franz, and Schiffer, Stefan. 2021. “On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations”. arXiv:2108.05757.
Behn, L., Gmeineder, F., and Schiffer, S. (2021). On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations. arXiv:2108.05757.
Behn, L., Gmeineder, F., & Schiffer, S., 2021. On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations. arXiv:2108.05757.
L. Behn, F. Gmeineder, and S. Schiffer, “On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations”, arXiv:2108.05757, 2021.
Behn, L., Gmeineder, F., Schiffer, S.: On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations. arXiv:2108.05757. (2021).
Behn, Linus, Gmeineder, Franz, and Schiffer, Stefan. “On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations”. arXiv:2108.05757 (2021).
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