Lower Semi-continuity of Integrals with G-quasiconvex Potential
نویسنده
چکیده
defined over Sobolev spaces is connected to the convexity of the potential w. In the scalar case, that is for functions u with domain or range in R, the functional I is weakly W 1,p lower semi-continuous (weakly * W ) if and only if w is convex, provided it is continuous and satisfies some growth conditions. The notion which replaces convexity in the vector case is quasi-convexity (introduced by Morrey [14]). We shall concentrate on the case u : Ω ⊂ R → R which is interesting for continuum media mechanics. Standard notation will be used, like:
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