Gradient estimates for solutions of elliptic systems with measurable coefficients from composite material

We study global gradient estimates for the weak solution to elliptic systems with measurable coefficients from composite materials in a nonsmooth bounded domain. The principal coefficients are assumed to be merely measurable in one variable and have small bounded mean oscillation (BMO) seminorms in...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2018-11, Vol.41 (16), p.7007-7031
Main Authors: Jang, Yunsoo, Kim, Youchan
Format: Article
Language:English
Subjects:
Coefficients
composite material
Composite materials
Domains
elliptic systems
Estimates
gradient estimates
measurable coefficients
Reifenberg flat domains
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Summary:We study global gradient estimates for the weak solution to elliptic systems with measurable coefficients from composite materials in a nonsmooth bounded domain. The principal coefficients are assumed to be merely measurable in one variable and have small bounded mean oscillation (BMO) seminorms in the other variables on each subdomain whose boundary satisfies the so‐called δ‐Reifenberg flat condition. Under these assumptions and based on our new geometric observation for disjoint Reifenberg domains in a previous study, we obtain global W1,p estimates.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5213