A lower semicontinuity result in BV is obtained for quasiconvex integrals with subquadratic growth. The key steps in this proof involve obtaining boundedness properties for an extension operator, and a precise blow-up technique that uses fine properties of Sobolev maps. A similar result is obtained by Kristensen in [Calc. Var. Partial Differ. Equ. 7 (1998) 249-261], where there are weaker asssumptions on convergence but the integral needs to satisfy a stronger growth condition.
Keywords: lower semicontinuity, quasiconvex integrals, functions of bounded variation
@article{COCV_2013__19_2_555_0,
author = {Soneji, Parth},
title = {Lower semicontinuity in {BV} of quasiconvex integrals with subquadratic growth},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {555--573},
year = {2013},
publisher = {EDP Sciences},
volume = {19},
number = {2},
doi = {10.1051/cocv/2012021},
mrnumber = {3049723},
zbl = {1263.49012},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2012021/}
}
TY - JOUR AU - Soneji, Parth TI - Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 555 EP - 573 VL - 19 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2012021/ DO - 10.1051/cocv/2012021 LA - en ID - COCV_2013__19_2_555_0 ER -
%0 Journal Article %A Soneji, Parth %T Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 555-573 %V 19 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2012021/ %R 10.1051/cocv/2012021 %G en %F COCV_2013__19_2_555_0
Soneji, Parth. Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 555-573. doi: 10.1051/cocv/2012021
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