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On an isotropic differential inclusion

TítuloOn an isotropic differential inclusion
Publication TypeUnpublished
Year of Publication2009
AuthorsBarroso AC, Croce G, Ribeiro AM
Series TitlePreprint
Palavras-chaveDifferential inclusion, isotropic set, rank one convexity, singular values
AbstractDifferential inclusions arise in successful models proposed to describe the microstructures of elastic crystals. In this paper we are interested in the existence of Lipschitz maps\\ u :Ω - R^2 satisfying the inclusion\\ Du ε E, a.e. in Ω\\ u = φ, on δΩ\\ where Ω is an open bounded subset of R^2 and E is a compactsubset of R^\{2×2\}, which is isotropic, that is to say, invariant under rotations. We will show an existence result under suitable hypotheses on the boundary datum φ..
URLhttp://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2009/8_09.pdf