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Résumé : We establish pointwise asymptotic estimates at infinity for solutions to the doubly weighted quasi-linear equation: { − div ( w 1 | ∇ u | p − 2 ∇ u ) = w 2 | u | q − 2 u in Ω , u ∈ D 1 , p , w 1 ( Ω ) , where w 1 and w 2 are compatible weights and q > p > 1 is a critical exponent in the sense of Sobolev.