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Journal Article

A-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals

Krämer J., Krömer S., Kružík Martin, Pathó G.

: Advances in Calculus of Variations vol.10, 1 (2017), p. 49-67

: GAP201/10/0357, GA ČR, GAP107/12/0121, GA ČR, CZ01-DE03/2013-2014/DAAD-56269992, GA AV ČR

: concentrations, oscillations, A-quasiconvexity

: 10.1515/acv-2015-0009

: Http://library.utia.cas.cz/separaty/2017/MTR/kruzik-0470210.pdf

(eng): We state necessary and sufficient conditions for weak lower semicontinuity of integral functionals of the form u bar right arrow integral(Omega) h(x, u(x)) dx, where h is continuous and possesses a positively p-homogeneous recession function, p > 1, and u is an element of L-p(Omega, R-m) lives in the kernel of a constant-rank first-order differential operator A which admits an extension property. In the special case A = curl, apart from the quasiconvexity of the integrand, the recession function's quasiconvexity at the boundary in the sense of Ball and Marsden is known to play a crucial role. Our newly defined notions of A-quasiconvexity at the boundary, generalize this result. Moreover, we give an equivalent condition for the weak lower semicontinuity of the above functional along sequences weakly converging in L-p(Omega, R-m) and approaching the kernel of A even if A does not have the extension property.

: BA

: 10101