Abstract
In this paper, we study the estimates of resolvents R(λ,Lε)=(Lε−λI)−1, where Lε=−div(A(x/ε)∇) is a family of second elliptic operators with symmetric, periodic and oscillating coefficients defined on a bounded domain Ω with ε>0. For 1<p<∞, we will establish uniform Lp→Lp, Lp→W01,p, W−1,p→Lp and W−1,p→W01,p estimates by using the real variable method. Meanwhile, we use Green functions for operators Lε−λI to study the asymptotic behavior of R(λ,Lε) and obtain convergence estimates in Lp→Lp, Lp→W01,p norm.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
