We study the lower semicontinuity properties and existence of a minimizer of the functional We introduce the notions of Morrey quasiconvexity, polyquasiconvexity, and rank-one quasiconvexity, all stemming from the notion of quasiconvexity (= convex level sets) of f in the last variable. We also for
Sets of lower semicontinuity and stability of integral functionals
โ Scribed by M.A. Sychev
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 233 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0021-7824
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๐ SIMILAR VOLUMES
We provide a sufficient condition which guarantees the lower-semicontinuity of the optimal solution set for a general nonlinear programming problem. It is shown that the same condition is both sufficient and necessary for convex programming problems that satisfy the Slater condition.
In this paper we show the weak lower semicontinuity of some classes of functionals, using the concentration-compactness principle of P. L. Lions. These functionals involve an integral term, and we do not know whether it can be handled by the De Giorgi theorem. The semicontinuity result allows us to