Homogenization and effective properties of plates weakened by partially penetrating fissures : convergence and duality
Determination of the potential form of operators
The author extends ideas of duality [see, for example, B. Noble and M. J. Sewell, J. Inst. Math. Appl. 9 (1972), 123–193; MR0307012] to a class of nonlinear operators on Banach spaces. Let U, V be Banach spaces and a(u,v) a bilinear form on U×V. Let N be a (nonlinear) operator N:U→V. GN(u)h denotes the Gâteaux derivative of N in the direction of h, computed at the point u∈U. Let us assume that a separates points in U×V (as defined by Marshall Stone). If there is v∈V such that a(h,v)=⟨h,Gf(u)⟩ for...
Review: P. Pedregal, Variational Methods in Nonlinear Elasticity
The article contains no abstract
Review: An Introduction to Homogenization
The article contains no abstract
Two-dimensional examples of rank-one convex functions that are not quasiconvex
The aim of this note is to provide two-dimensional examples of rank-one convex functions which are not quasiconvex.
Young measures and their applications in micromechanics and optimization. I. Mathematical principles.
The paper is a review of modern mathematical methods for the analysis of continuous problems of nonlinear mechanics and magnetism. The bibliography contains 175 items. The second part of the paper deals with mechanical problems described by nonconvex density energy functions and with numerical methods to solve such problems.
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