Universität zu Köln

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:	Creators Email ORCID ORCID Put Code Kraemer, Jan UNSPECIFIED UNSPECIFIED UNSPECIFIED Kroemer, Stefan UNSPECIFIED UNSPECIFIED UNSPECIFIED Kruzik, Martin UNSPECIFIED orcid.org/0000-0003-1558-5809 UNSPECIFIED Patho, Gabriel UNSPECIFIED UNSPECIFIED UNSPECIFIED
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:	Keywords Language QUASI-CONVEXITY; OSCILLATIONS; CONVERGENCE; RELAXATION; CONTINUITY; SEQUENCES Multiple languages Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/24285