| Title | On an isotropic differential inclusion |
| Publication Type | Unpublished |
| Year of Publication | 2009 |
| Authors | Barroso AC, Croce G, Ribeiro AM |
| Series Title | Preprint |
| Keywords | Differential inclusion, isotropic set, rank one convexity, singular values |
| Abstract | Differential 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.. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2009/8_09.pdf |