For every finite nonnegative measure ft we introduce the Sobolev spaces W^'(Q,K) and we study the lower semicontinuity of functionals of the form where the integrand / is quasiconvex.

In this paper, we investigate the continuity of attractors in time-dependent phase spaces. (i) We establish two abstract criteria on upper semicontinuity and residual pullback D-attractor with respect to perturbations, an equivalence criterion between their equi-attraction, which generalize theory developed recently [27], [28] that (ii) propose notion D-exponential attractor, includes exponenti...

In this paper,we consider a parametric generalized vector quasiequilibriumproblemwhich is mixed in the sense that several different relations can simultaneously appear in this problem. The moving cones and other data of the problem are assumed to be set-valued maps defined in topological spaces and taking values in topological spaces or topological vector spaces. The main result of this paper g...

Lower semicontinuity properties of multiple integrals u ∈W (Ω;R) 7→ ∫ Ω f(x, u(x), · · · ,∇u(x)) dx are studied when f may grow linearly with respect to the highest-order derivative, ∇ku, and admissible W k,1(Ω;Rd) sequences converge strongly in W k−1,1(Ω;Rd). It is shown that under certain continuity assumptions on f, convexity, 1-quasiconvexity or k-polyconvexity of ξ 7→ f(x0, u(x0), · · · ,∇...