On symmetric div-quasiconvex hulls and divsym-free $\mathrm{L}^\infty$-truncations

Abstract

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 .