Universität zu Köln

Benesova, Barbora ORCID: 0000-0002-6083-247X, Kroemer, Stefan and Kruzik, Martin ORCID: 0000-0003-1558-5809 (2015). BOUNDARY EFFECTS AND WEAK* LOWER SEMICONTINUITY FOR SIGNED INTEGRAL FUNCTIONALS ON BV. ESAIM-Control OPtim. Calc. Var., 21 (2). S. 513 - 535. LES ULIS CEDEX A: EDP SCIENCES S A. ISSN 1262-3377

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Abstract

We characterize lower semicontinuity of integral functionals with respect to weak* convergence in BV, including integrands whose negative part has linear growth. In addition, we allow for sequences without a fixed trace at the boundary. In this case, both the integrand and the shape of the boundary play a key role. This is made precise in our newly found condition - quasi-sublinear growth from below at points of the boundary - which compensates for possible concentration effects generated by the sequence. Our work extends some recent results by Kristensen and Rindler [J. Kristensen and F. Rindler, Arch. Rat. Mech. Anal. 197 (2010) 539-598; J. Kristensen and F. Rindler, Calc. Var. 37 (2010) 29-62].

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Benesova, Barbora UNSPECIFIED orcid.org/0000-0002-6083-247X UNSPECIFIED Kroemer, Stefan UNSPECIFIED UNSPECIFIED UNSPECIFIED Kruzik, Martin UNSPECIFIED orcid.org/0000-0003-1558-5809 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-408576
DOI:	10.1051/cocv/2014036
Journal or Publication Title:	ESAIM-Control OPtim. Calc. Var.
Volume:	21
Number:	2
Page Range:	S. 513 - 535
Date:	2015
Publisher:	EDP SCIENCES S A
Place of Publication:	LES ULIS CEDEX A
ISSN:	1262-3377
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language QUASICONVEXITY; GRADIENTS; OSCILLATIONS; RELAXATION; SEQUENCES Multiple languages Automation & Control Systems; Mathematics, Applied Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/40857