We establish that for any non-empty, compact set the - and -symmetric div-quasiconvex hulls and 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 -truncation that preserves both symmetry and solenoidality of matrix-valued maps in . For comparison, we moreover give a construction of -free truncations in the regime which, however, does not apply to the case .
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Linus Behn, Franz Gmeineder, Stefan Schiffer, On symmetric div-quasiconvex hulls and divsym-free -truncations. Ann. Inst. H. Poincaré Anal. Non Linéaire (2022),DOI 10.4171/AIHPC/66