Universität zu Köln

Kreisbeck, Carolin and Kromer, Stefan (2016). HETEROGENEOUS THIN FILMS: COMBINING HOMOGENIZATION AND DIMENSION REDUCTION WITH DIRECTORS. SIAM J. Math. Anal., 48 (2). S. 785 - 821. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7154

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Abstract

We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely, the film thickness and the period of oscillating microstructures, by means of Gamma-convergence. On a technical level, this requires a subtle merging of homogenization tools, such as multiscale convergence methods, with dimension reduction techniques for functionals subject to differential constraints. One observes that the results depend critically on the relative magnitude between the two scales. Interestingly, this even regards the fundamental question of locality of the limit model and, in particular, leads to new findings also in the gradient case.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kreisbeck, Carolin UNSPECIFIED UNSPECIFIED UNSPECIFIED Kromer, Stefan UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-293424
DOI:	10.1137/15M1032557
Journal or Publication Title:	SIAM J. Math. Anal.
Volume:	48
Number:	2
Page Range:	S. 785 - 821
Date:	2016
Publisher:	SIAM PUBLICATIONS
Place of Publication:	PHILADELPHIA
ISSN:	1095-7154
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language HIGHER-ORDER PERTURBATIONS; 2-SCALE CONVERGENCE; EQUI-INTEGRABILITY; A-QUASICONVEXITY; RELAXATION; FUNCTIONALS; SEMICONTINUITY; VECTOR Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/29342