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. Le-syst-eme, 48) est une formulation variationnelle d'un probl eme elliptique semi-lin eaire, et puisque n e ue et p e ue sont dans W 1;1 (() alors (5.48) admet une solution unique not ee, pp.3-5

. Comme-la-quantit-e-e-ue-+-e-ue, qui appara^ t dans la premi ere equation de (5.47), est minor ee par une constante strictement positive, nous en d eduisons que le probl eme (5.47) poss ede une unique solution (' 1, 3 ) 2 (H 2 DN (()) 3 qui d epend contin^ ument de

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