# Dimension reduction for functionals on solenoidal vector fields

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 1, page 259-276
- ISSN: 1292-8119

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topKrömer, Stefan. "Dimension reduction for functionals on solenoidal vector fields." ESAIM: Control, Optimisation and Calculus of Variations 18.1 (2012): 259-276. <http://eudml.org/doc/272915>.

@article{Krömer2012,

abstract = {We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint can give rise to a nonlocal functional as illustrated in an example.},

author = {Krömer, Stefan},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {divergence-free fields; gamma-convergence; dimension reduction; -convergence},

language = {eng},

number = {1},

pages = {259-276},

publisher = {EDP-Sciences},

title = {Dimension reduction for functionals on solenoidal vector fields},

url = {http://eudml.org/doc/272915},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Krömer, Stefan

TI - Dimension reduction for functionals on solenoidal vector fields

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2012

PB - EDP-Sciences

VL - 18

IS - 1

SP - 259

EP - 276

AB - We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint can give rise to a nonlocal functional as illustrated in an example.

LA - eng

KW - divergence-free fields; gamma-convergence; dimension reduction; -convergence

UR - http://eudml.org/doc/272915

ER -

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