TY - JOUR
T1 - Two-parameter anisotropic homogenization for a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain
T2 - A functional analytic approach
AU - de Cristoforis, Massimo Lanza
AU - Musolino, Paolo
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We consider a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ, and the level of anisotropy of the cell is determined by a diagonal matrix γ with positive diagonal entries. The relative size of each periodic perforation is instead determined by a positive parameter ε. For a given value math formula of γ, we analyze the behavior of the unique solution of the problem as math formula tends to math formula by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.
AB - We consider a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ, and the level of anisotropy of the cell is determined by a diagonal matrix γ with positive diagonal entries. The relative size of each periodic perforation is instead determined by a positive parameter ε. For a given value math formula of γ, we analyze the behavior of the unique solution of the problem as math formula tends to math formula by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.
KW - anisotropic homogenization
KW - Dirichlet problem
KW - integral equations
KW - Poisson equation
KW - periodically perforated domain
KW - real analytic continuation in Banach space
KW - singularly perturbed domain
U2 - 10.1002/mana.201600414
DO - 10.1002/mana.201600414
M3 - Article
SN - 0025-584X
VL - 291
SP - 1310
EP - 1341
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 8-9
ER -