Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth

Parth Soneji

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 2, page 555-573
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Soneji, Parth. "Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth." ESAIM: Control, Optimisation and Calculus of Variations 19.2 (2013): 555-573. <http://eudml.org/doc/272795>.

@article{Soneji2013,
abstract = {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.},
author = {Soneji, Parth},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {lower semicontinuity; quasiconvex integrals; functions of bounded variation},
language = {eng},
number = {2},
pages = {555-573},
publisher = {EDP-Sciences},
title = {Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth},
url = {http://eudml.org/doc/272795},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 2
SP - 555
EP - 573
AB - 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.
LA - eng
KW - lower semicontinuity; quasiconvex integrals; functions of bounded variation
UR - http://eudml.org/doc/272795
ER -

References

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