no. 6
On symmetric div-quasiconvex hulls and divsym-free L ∞ -truncations
Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 6, pp. 1267-1317
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We establish that for any non-empty, compact set K⊂ℝ sym 3×3 the 1- and ∞-symmetric div-quasiconvex hulls K (1) and K (∞) coincide. This settles a conjecture in a recent work of Conti,Müller & Ortiz [Arch. Ration. Mech. Anal. 235 (2020)] in the affirmative. As a key novelty, we construct an L ∞ -truncation that preserves both symmetry and solenoidality of matrix-valued maps in L 1 . For comparison, we moreover give a construction of 𝒜 -free truncations in the regime 1<p<∞ which, however, does not apply to the case p=1.

Publié le :
DOI : 10.4171/aihpc/66
Classification : 26B25, 49J45
Keywords: divsym-quasiconvexity, A-quasiconvexity, convex hulls, differential constraints, divergence-free truncation, A-free truncation 
@article{AIHPC_2023__40_6_1267_0,
     author = {Behn, Linus and Gmeineder, Franz and Schiffer, Stefan},
     title = {On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1267--1317},
     year = {2023},
     volume = {40},
     number = {6},
     doi = {10.4171/aihpc/66},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpc/66/}
}
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Behn, Linus; Gmeineder, Franz; Schiffer, Stefan. On symmetric div-quasiconvex hulls and divsym-free $L^\infty$-truncations. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 6, pp. 1267-1317. doi: 10.4171/aihpc/66

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