On some definitions and properties of generalized convex sets arising in the calculus of variations

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Abstract

We deal with generalized notions of convexity for sets. Namely, thepolyconvexity, quasiconvexity, rank one convexity and separate convexity. The question has its origin in the calculus of variations. We try tosystematize the results concerning these generalized notions imitating asmuch as possible the classical approach of convex analysis. Throughoutthe article, we will discuss the relations between the different convexities,separation and Carath´eodory type theorems, the notion of hull of a setand extremal points.
Original languageEnglish
Title of host publicationRecent Advances on Elliptic and Parabolic Issues
Subtitle of host publicationProceedings of the 2004 Swiss-Japanese Seminar, Zurich, Switzerland, 6 – 10 December 2004
EditorsMichel Chipot, Hirokazu Ninomiya
Place of PublicationSingapore
PublisherWorld Scientific
Pages103-128
Number of pages26
ISBN (Electronic)978-981-4472-99-9
ISBN (Print)978-981-256-675-1
DOIs
Publication statusPublished - 2006
Event2004 Swiss-Japanese Seminar - Zurique, Switzerland
Duration: 6 Dec 200410 Dec 2004

Seminar

Seminar2004 Swiss-Japanese Seminar
CountrySwitzerland
CityZurique
Period6/12/0410/12/04

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