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Approximate Conditions and Passage to the Limit in Sobolev Spaces over Thin and Composite Structures
S. E. Pastukhova 《Journal of Mathematical Sciences》2006,133(1):931-948
Approximate properties of variable measures compose a base of the two-scale convergence method with respect to a variable
measure, which is used in averaging on periodic thin and composite structures. The paper gives a survey of methods for verifying
approximate properties. The main focus is on studying composite measures, which have been little studied.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 16, Partial
Differential Equations, 2004. 相似文献
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Korn-type inequalities for thin periodic structures of period and width h() with h() 0 are presented. Periodic meshes, three-dimensional road structures, and three-dimensional box structures are considered. A particular attention is paid to structures with the so-called critical width when
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Within the framework of the theory of Γ-convergence for convex functionals with nonstandard coercivity and growth conditions,
we study the inheritance of some properties (for example, strict convexity, differentiablility, and Δ2-property) of integrands under taking the Γ-closure. We focus on power integrands |ξ|
p(x)
with variable exponents. The results obtained are also of interest in the case of the Γ-convergence theory for standard functionals.
Bibliography: 15 titles. 相似文献
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