The “strange term” in the periodic homogenization for multivalued Leray–Lions operators in perforated domains

Using the periodic unfolding method of Cioranescu, Damlamian and Griso, we study the homogenization for equations of the form in a perforated domain with holes of size periodically distributed in the domain, where is a function whose values are maximal monotone graphs (on R N ). Two different unfold...

Full description

Saved in:
Bibliographic Details
Published in:Ricerche di matematica 2010-12, Vol.59 (2), p.281-312
Main Authors: Damlamian, Alain, Meunier, Nicolas
Format: Article
Language:English
Subjects:
Algebra
Analysis
Analysis of PDEs
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Using the periodic unfolding method of Cioranescu, Damlamian and Griso, we study the homogenization for equations of the form in a perforated domain with holes of size periodically distributed in the domain, where is a function whose values are maximal monotone graphs (on R N ). Two different unfolding operators are involved in such a geometric situation. Under appropriate growth and coercivity assumptions, if the corresponding two sequences of unfolded maximal monotone graphs converge in the graph sense to the maximal monotone graphs A ( x , y ) and A 0 ( x , z ) for almost every , as , then every cluster point ( u 0 , d 0 ) of the sequence for the weak topology in the naturally associated Sobolev space is a solution of the homogenized problem which is expressed in terms of u 0 alone. This result applies to the case where is of the form where B ( y ) is periodic and continuous at y  = 0, and, in particular, to the oscillating p -Laplacian.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-010-0087-4