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Determination of the potential form of operators

J. J. Telega — 1982

Mathematica Applicanda

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...

Young measures and their applications in micromechanics and optimization. I. Mathematical principles.

W. BielskiE. KruglenkoJ. J. Telega — 2003

Mathematica Applicanda

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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