Homogenization of locally periodic parabolic operators with non-self-similar scales
Jun Geng, Weisheng Niu · arXiv (Cornell University) · 2021
We investigate quantitative estimates in homogenization of the locally periodic parabolic operator with multiscales $$ \partial_t- \text{div} (A(x,t,x/\varepsilon,t/κ^2) abla ),\qquad \varepsilon>0,\, κ>0. $$ Under proper assumptions, we establish the full-scale interior and boundary Lipschitz estimates. These results are new even for the case $κ=\varepsilon$, and for the periodic operators $ \partial_t-\text{div}(A(x/\varepsilon, t/\varepsilon^{\ell}) abla ),$ $0