We prove a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps u : ⊂ R^n → R^m in W^{1,m} , 2 ≤ m ≤ n, bounded in W^{1,m−1} and convergent in L^1 under mild technical conditions but without any extra coercivity assumption on the integrand.
Weak lower semicontinuity for polyconvex integrals in the limit case / M. Focardi;N. Fusco;C. Leone;P. Marcellini;E. Mascolo;A. Verde. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - ELETTRONICO. - 51:(2014), pp. 171-193. [10.1007/s00526-013-0670-0]
Weak lower semicontinuity for polyconvex integrals in the limit case
FOCARDI, MATTEO;MARCELLINI, PAOLO;MASCOLO, ELVIRA;
2014
Abstract
We prove a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps u : ⊂ R^n → R^m in W^{1,m} , 2 ≤ m ≤ n, bounded in W^{1,m−1} and convergent in L^1 under mild technical conditions but without any extra coercivity assumption on the integrand.
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