Geodesic
A differential inclusion : the case of an isotropic set
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 122-138

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In this article we are interested in the following problem: to find a map u:Ω→ℝ 2 that satisfies

Du∈Ea.e.inΩu(x)=ϕ(x)x∈∂Ω
where Ω is an open set of ℝ 2 and E is a compact isotropic set of ℝ 2×2 . We will show an existence theorem under suitable hypotheses on ϕ.

DOI : 10.1051/cocv:2004035
Classification : 34A60, 35F30, 52A30
Keywords: rank one convex hull, polyconvex hull, differential inclusion, isotropic set 
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     title = {A differential inclusion : the case of an isotropic set},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {122--138},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {1},
     year = {2005},
     doi = {10.1051/cocv:2004035},
     mrnumber = {2110617},
     zbl = {1092.34004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004035/}
}
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Croce, Gisella. A differential inclusion : the case of an isotropic set. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 122-138. doi: 10.1051/cocv:2004035

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