Lower-Semicontinuity of Variational Integrals and Compensated Compactness

Vladimír Šverák
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Vladimír Šverák: University of Minnesota, Department of Mathematics

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 1153-1158 from Springer

Abstract: Abstract We consider variational integrals $$ I(u) = \int_\Omega {f(Du(x))dx}$$ defined for (sufficiently regular) functionsu: Ω →R m . Here Ω is a bounded open subset ofR n ,Du(x) denotes the gradient matrix ofu atx, andf:Mm×n →R is given,Mm×n denoting the space of real (m ×n)-matrices. We are interested in the casem, n ≥ 2.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_108

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