@Article{JPDE-37-2,
author = {Tian, Hong and Shuai, Hao and Zheng, Shenzhou},
title = {$W^{m,p(t,x)}$-Estimate for a Class of Higher-Order Parabolic Equations with Partially BMO Coefficients},
journal = {Journal of Partial Differential Equations},
year = {2024},
volume = {37},
number = {2},
pages = {198--234},
abstract = {<p style="text-align: justify;">We prove a global estimate in the Sobolev spaces with variable exponents to
the solution of a class of higher-order divergence parabolic equations with measurable
coefficients over the non-smooth domains. Here, it is mainly assumed that the coefficients are allowed to be merely measurable in one of the spatial variables and have
a small BMO quasi-norm in the other variables at a sufficiently small scale, while the
boundary of the underlying domain belongs to the so-called Reifenberg flatness. This
is a natural outgrowth of Dong-Kim-Zhang’s papers [1, 2] from the $W^{m,p}$-regularity
to the $W^{m,p(t,x)}$-regularity for such higher-order parabolic equations with merely measurable coefficients with Reifenberg flat domain which is beyond the Lipschitz domain
with small Lipschitz constant.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v37.n2.6},
url = {https://global-sci.com/article/91204/wmptx-estimate-for-a-class-of-higher-order-parabolic-equations-with-partially-bmo-coefficients}
}