We establish that for any non-empty, compact set K\subset\mathbb{R}_{\operatorname{sym}}^{3\times 3} the 1 - and \infty -symmetric div-quasiconvex hulls \smash{K^{(1)}} and \smash{K^{(\infty)}} 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 \operatorname{L}^{\infty} -truncation that preserves both symmetry and solenoidality of matrix-valued maps in \operatorname{L}^{1} . For comparison, we moreover give a construction of \mathcal{A} -free truncations in the regime 1<p<\infty which, however, does not apply to the case p=1 .

We establish that for any non-empty, compact set K ⊂ R 3×3 sym the 1-and ∞-symmetric div-quasiconvex hulls K (1) and K (∞) coincide. This settles a conjecture in a recent work of Conti, Müller & Ortiz [10] in the affirmative. As a key novelty, we construct an L ∞ -truncation that preserves both symmetry and solenoidality of matrixvalued maps in L 1 .