Introduction to the theory of two-scale convergence

DOI10.1007/s10958-014-1717-2zbMath1328.46029OpenAlexW2041071506MaRDI QIDQ460518

G. A. Iosif'yan, Vasilii V. Jikov

Publication date: 13 October 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-014-1717-2

zbMATH Keywords

weak convergenceSobolev spaceshomogenizationspectral problemsweak compactnesselliptic operatorsLebesgue spacestwo-scale convergence

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Applications of operator theory to differential and integral equations (47N20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Compactness in Banach (or normed) spaces (46B50) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (6)

Convergence of monotone operators with respect to measures ⋮ Non-local effects by homogenization or 3D-1D dimension reduction in elastic materials reinforced by stiff fibers ⋮ Homogenization of the equations of filtration of a viscous fluid in two porous media ⋮ On homogenized equations of filtration in two domains with common boundary ⋮ Elliptic operators with nonstandard growth condition: Some results and open problems ⋮ On applications of Herglotz-Nevanlinna functions in material sciences. II: Extended applications and generalized theory

Cites Work

• Unnamed Item
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• Homogenization and porous media
• Energies with respect to a measure and applications to low dimensional structures
• Derivation of the Double Porosity Model of Single Phase Flow via Homogenization Theory
• On the Convergence of the Energy, Stress Tensors, and Eigenvalues in Homogenization Problems of Elasticity
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• On an extension of the method of two-scale convergence and its applications
• On two-scale convergence
• The homogenization of nonstationary equations with contrast coefficients.

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