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Boundary effects and weak* lower semicontinuity for signed integral functionals on BV

Journal Article

Benešová B., Kroemer S., Kružík Martin

serial: ESAIM-Control Optimisation and Calculus of Variations vol.21, 2 (2015), p. 513-534

project(s): GAP201/10/0357, GA ČR

keywords: lower semicontinuity, quasiconvexity

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abstract (eng):

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.


2012-12-21 16:10