| 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. |
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