TY - JOUR
T1 - Convergence Rates in L 2 for Elliptic Homogenization Problems
AU - Kenig, Carlos E.
AU - Lin, Fanghua
AU - Shen, Zhongwei
N1 - Funding Information:
Carlos E. Kenig was supported in part by NSF grant DMS-0968472. Fanghua Lin was supported in part by NSF grant DMS-0700517. Zhongwei Shen was supported in part by NSF grant DMS-0855294.
PY - 2012/3
Y1 - 2012/3
N2 - We study rates of convergence of solutions in L 2 and H 1/2 for a family of elliptic systems {L e{open}} with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of {L e{open}}. Most of our results, which rely on the recently established uniform estimates for the L 2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867-917, 2011; Commun Pure Appl Math 64:1-44, 2011) are new even for smooth domains.
AB - We study rates of convergence of solutions in L 2 and H 1/2 for a family of elliptic systems {L e{open}} with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of {L e{open}}. Most of our results, which rely on the recently established uniform estimates for the L 2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867-917, 2011; Commun Pure Appl Math 64:1-44, 2011) are new even for smooth domains.
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U2 - 10.1007/s00205-011-0469-0
DO - 10.1007/s00205-011-0469-0
M3 - Article
AN - SCOPUS:84856710178
VL - 203
SP - 1009
EP - 1036
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 3
ER -