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The principal subject of this thesis is the study of some Dirichlet problems related to differential inclusions of first and second order. We have studied the two following problems : where E ⊂ R2×2 is a compact isotropic set and where We show some existence theorems of W1,∞ and W2,∞ solutions respectively. Moreover we have studied a minimization problem : the computation of α(p, q, r) defined by
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