A - Quasiconvexity , Lower Semicontinuity And
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منابع مشابه
Quasiconvexity versus Group Invariance
The lower invariance under a given arbitrary group of diffeomorphisms extends the notion of quasiconvexity. The non-commutativity of the group operation (the function composition) modifies the classical equivalence between lower semicontinuity and quasiconvexity. In this context null lagrangians are particular cases of integral invariants of the group.
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We fully characterize quasiconvex hulls for three arbitrary solenoidal (divergence free) wells in dimension three. With this aim we establish weak lower semicontinuity of certain functionals with integrands restricted to generic twodimensional planes and convex in (up to three) rank-2 directions within the planes. Within the framework of the theory of compensated compactness, the latter represe...
متن کاملOn a Restricted Weak Lower Semicontinuity for Smooth Functional on Sobolev Spaces
We study a restricted weak lower semicontinuity property, which we call the (PS)-weak lower semicontinuity, for a smooth integral functional on the Sobolev space along all weakly convergent Palais-Smale sequences of the functional. By the Ekeland variational principle, the (PS)-weak lower semicontinuity is sufficient for the existence of minimizers under the usual coercivity assumption. In gene...
متن کاملK-quasiconvexity Reduces to Quasiconvexity
The relation between quasiconvexity and k-quasiconvexity, k ≥ 2, is investigated. It is shown that every smooth strictly k-quasiconvex integrand with p-growth at infinity, p > 1, is the restriction to k-th order symmetric tensors of a quasiconvex function with the same growth. When the smoothness condition is dropped, it is possible to prove an approximation result. As a consequence, lower semi...
متن کاملOn a Restricted Weak Lower Semicontinuity for Smooth Functionals on Sobolev Spaces
This paper is motivated by a problem suggested in Müller [11] that concerns the weak lower semicontinuity of a smooth integral functional I(u) on a Sobolev space along all its weakly convergent minimizing sequences. Here we study a restricted weak lower semicontinuity of I(u) along all weakly convergent Palais-Smale sequences (that is, sequences {uk} satisfying I′(uk)→ 0). In view of Ekeland’s ...
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