首页|Wm,p(t,x)-Estimate for a Class of Higher-Order Parabolic Equations with Partially BMO Coefficients
Wm,p(t,x)-Estimate for a Class of Higher-Order Parabolic Equations with Partially BMO Coefficients
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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 coef-ficients 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 Wm,p-regularity to the Wm,p(t,x)-regularity for such higher-order parabolic equations with merely mea-surable coefficients with Reifenberg flat domain which is beyond the Lipschitz domain with small Lipschitz constant.
A higher-order parabolic equationSobolev spaces with variable exponentspartially BMO quasi-normReifenberg flat domainslog-Hölder continuity
TIAN Hong、HAO Shuai、ZHENG Shenzhou
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College of Science,Tianjin University of Technology,Tianjin 300384,China
Department of Mathematics,Beijing Jiaotong University,Beijing 100044,China
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