NDLI: Boundary effects and weak⋆ lower semicontinuity for signed integral functionals on BV

Content Provider	EDP Sciences
Author	Barbora Benešová Stefan Krömer Martin Kružík
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].}}
Ending Page	534
Starting Page	513
Page Count	22
File Format	HTM / HTML PDF
ISSN	12928119
Alternate Webpage(s)	https://www.esaim-cocv.org/articles/cocv/abs/2015/02/cocv140036/cocv140036.html
e-ISSN	12623377
Issue Number	2
Journal	ESAIM: Control, Optimisation and Calculus of Variations
Volume Number	21
DOI	10.1051/cocv/2014036
Language	English
Publisher	EDP Sciences
Publisher Date	2015-04-01
Access Restriction	Subscribed
Rights Holder	© EDP Sciences, SMAI, 2015
Subject Keyword	Lower semicontinuity BV quasiconvexity free boundary Lower semicontinuity / BV / quasiconvexity / free boundary Methods involving semicontinuity and convergence; relaxation Absolutely continuous functions, functions of bounded variation
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Computational Mathematics

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