Abstract
In this paper, we extend the uniform regularity estimates obtained by M. Avellaneda and F. Lin in [3,6] to the more general second order elliptic systems in divergence form {Lε,ε>0}, with rapidly oscillating periodic coefficients. We establish not only sharp W1,p estimates, Hölder estimates, Lipschitz estimates and non-tangential maximal function estimates for the Dirichlet problem on a bounded C1,η domain, but also a sharp O(ε) convergence rate in H01(Ω) by virtue of the Dirichlet correctors. Moreover, we define the Green's matrix associated with Lε and obtain its decay estimates. We remark that the well known compactness methods are not employed here, instead we construct the transformations (1.11) to make full use of the results in [3,6].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.