Special Session 15: Qualitative properties for solutions to nonlinear elliptic and parabolic equations

Uniform Calder\`{o}n-Zygmund estimates in multiscale elliptic homogenization
Weisheng Niu
Anhui University
Peoples Rep of China
Co-Author(s):    Jinping Zhuge
Abstract:
We report some recent results on the uniform Calderon-Zygmund estimate in the homogenization of elliptic equations with multiscales. Our result includes the uniform Calderon-Zygmund estimate in quasiperiodic elliptic homogenization (even without the Diophantine condition), which was previously unknown. The proof combines the Dirichlet`s theorem on the simultaneous Diophantine approximation from number theory, a technique of reperiodization, reiterated periodic homogenization and a large-scale real-variable argument. This a joint work with Jinping Zhuge.