Boundary effects and weak$^*$ lower semicontinuity for signed integral functionals on $\mathrm{BV}$
Analysis of PDEs
2015-01-27 v1
Abstract
We characterize lower semicontinuity of integral functionals with respect to weak convergence in , 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 J. Kristensen and F. Rindler (Arch. Rat. Mech. Anal. 197 (2010), 539--598 and Calc. Var. 37 (2010), 29--62).
Cite
@article{arxiv.1405.0449,
title = {Boundary effects and weak$^*$ lower semicontinuity for signed integral functionals on $\mathrm{BV}$},
author = {Barbora Benešová and Stefan Krömer and Martin Kružík},
journal= {arXiv preprint arXiv:1405.0449},
year = {2015}
}