Green's matrices and boundary estimates in parabolic homogenization

Geng, Jun; Shi, Bojing

doi:10.1016/j.jde.2020.02.021

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2023

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“…As the prototype, quantitative estimates in homogenization of the following operator ∂ t − div A(x/ε, t/ε 2 )∇ (1.6) have been largely studied. The uniform interior and boundary Lipschitz estimates were established in [11] and [15], while the convergence rates have been studied in different contexts in [12,32,23]. See also [20,22,1,13] for more related results.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of Parabolic Equations with Non-self-similar Scales

Geng¹,

Shen²

2019

Arch Rational Mech Anal

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This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in different scales. We obtain large-scale interior and boundary Lipschitz estimates as well as interior C 1,α and C 2,α estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems.MSC2010: 35B27, 35K40.

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