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On etudie les solutions singulieres de l'equation div(Dv/(1+|Dv| 2 ) 1/2 )=Kv dans R N avec K<0. On demontre l'existence globale d'une solution a symetrie rotationnelle. On demontre l'unicite d'une solution symetrique negative et concave pres de l'origine

Global existence and uniqueness results for singular solutions of the capillarity equation