Kraemer, Jan, Kroemer, Stefan, Kruzik, Martin ORCID: 0000-0003-1558-5809 and Patho, Gabriel (2017). A-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals. Adv. Calc. Var., 10 (1). S. 49 - 68. BERLIN: WALTER DE GRUYTER GMBH. ISSN 1864-8266

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Abstract

We state necessary and sufficient conditions for weak lower semicontinuity of integral functionals of the form u bar right arrow integral(Omega) h(x, u(x)) dx, where h is continuous and possesses a positively p-homogeneous recession function, p > 1, and u is an element of L-p(Omega; R-m) lives in the kernel of a constant-rank first-order differential operator A which admits an extension property. In the special case A = curl, apart from the quasiconvexity of the integrand, the recession function's quasiconvexity at the boundary in the sense of Ball and Marsden is known to play a crucial role. Our newly defined notions of A-quasiconvexity at the boundary, generalize this result. Moreover, we give an equivalent condition for the weak lower semicontinuity of the above functional along sequences weakly converging in L-p(Omega; R-m) and approaching the kernel of A even if A does not have the extension property.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Kraemer, JanUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Kroemer, StefanUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Kruzik, MartinUNSPECIFIEDorcid.org/0000-0003-1558-5809UNSPECIFIED
Patho, GabrielUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-242853
DOI: 10.1515/acv-2015-0009
Journal or Publication Title: Adv. Calc. Var.
Volume: 10
Number: 1
Page Range: S. 49 - 68
Date: 2017
Publisher: WALTER DE GRUYTER GMBH
Place of Publication: BERLIN
ISSN: 1864-8266
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
QUASI-CONVEXITY; OSCILLATIONS; CONVERGENCE; RELAXATION; CONTINUITY; SEQUENCESMultiple languages
Mathematics, Applied; MathematicsMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/24285

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