Lower semicontinuity for nonautonomous surface integrals

On the Lower Semicontinuity of Quasiconvex Integrals

In this paper, dedicated to Neil Trudinger in the occasion of his 70 birthday, we propose a relatively elementary proof of the weak lower semicontinuity in W 1,p of a general integral of the Calculus of Variations of the type (1.1) below with a quasiconvex density function satisfying p-growth conditions. Several comments and references on the related literature, and a subsection devoted to some...

Lower Semicontinuity in SBV for Integrals with Variable Growth

We prove a lower semicontinuity result for free discontinuity energies with a quasiconvex volume term having non standard growth and a surface term.

Lower semicontinuity of surface energies

Weak Lower Semicontinuity for Polyconvex Integrals in the Limit Case

We prove a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps u : Ω ⊂ R → R in W , 2 ≤ m ≤ n, bounded in W 1,m−1 and convergent in L under mild technical conditions but without any extra coercivity assumption on the integrand.

Approximation of Quasiconvex Functions, and Lower Semicontinuity of Multiple Integrals

We study semicontinuity of multiple integrals ~ f~,u,Du)dx~ where the vector-valued function u is defined for xE ~C N with values in ~ . The function f(x,s,~) is assumed to be Carath@odory and quasiconvex in Morrey's sense. We give conditions on the growth of f that guarantee the sequential lower semicontinuity of the given integral in the weak topology 1 N of the Sobolev space H 'P(~;~ ). The ...