Approximation of resolvents in homogenization of fourth-order elliptic operators
S. E. Pastukhova
Abstract
Abstract We study the homogenization of a fourth-order divergent elliptic operator with rapidly oscillating -periodic coefficients, where is a small parameter. The homogenized operator is of the same type and has constant coefficients. We apply Zhikov’s shift method to obtain an estimate in the -operator norm of order for the difference of the resolvents and . Bibliography: 25 titles.
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MathematicsHomogenization (climate)Constant coefficientsElliptic operatorOperator (biology)Semi-elliptic operatorOperator normNorm (philosophy)Mathematical analysisOrder (exchange)Pure mathematicsApplied mathematicsOperator theoryDifferential operatorChemistryLawRepressorBiologyBiodiversityEcologyEconomicsFinanceTranscription factorPolitical scienceBiochemistryGeneAdvanced Mathematical Modeling in EngineeringAdvanced Numerical Methods in Computational MathematicsComposite Material Mechanics