0646631 20260226111637.320260226235959.9 105030300067 10.1007/s00526-026-03262-z 10 s. P cav_un_epca*02523290944-266965Springer polyconvexity double well integral function cav_un_auth*0015534 Henrion D. FR cav_un_auth*0101142 Kružík Martin UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR 50 K Ústav teorie informace a automatizace AV ČR, v. v. i. https://library.utia.cas.cz/separaty/2026/MTR/kruzik-0646631.pdf https://link.springer.com/article/10.1007/s00526-026-03262-z GA24-10366S GA ČR CZ cav_un_auth*0472839 We investigate polyconvexity of the double well function f(X):=|X-X1|2|X-X2|2 for given matrices X1,X2∈Rn×n. Such functions are fundamental in the modeling of phase transitions in materials, but their non-convex nature presents challenges for the analysis of variational problems. Polyconvexity of f is related to the singular values of the matrix difference X1-X2. We prove that f is polyconvex if and only if the square of the largest singular value does not exceed the sum of the squares of the other singular values. This condition allows the function to be decomposed into the sum of a strictly convex part and a null Lagrangean. As a direct application of this result, we prove an existence and uniqueness theorem for the corresponding Dirichlet minimization problem of the integral functional. 2027 BA WOS 10000 10100 10102 2 RVO:67985556 https://hdl.handle.net/11104/0376330 S 88 A MATHEMATICS.APPLIED|MATHEMATICS 2.4 0.5 7.4 0.01644 1.845 6551 87 2.405 35.34 1.98 1550 Q1 1.900 245 Q1 87.2 1.48 Q1 93 2026 105030300067 SCOPUS PUBMED WOS cav_un_epca*0252329 Calculus of Variations and Partial Differential Equations Roč. 65 č. 3 2026 0944-2669 1432-0835 Springer