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We consider the problem of the minimization of the p-compliance functional where the control variables Σ are taking among closed connected one-dimensional sets. we prove some estimate from below of the p-compliance functional in terms of the one-dimensional Hausdorff measure of Σ and compute the value of the constant θ(p) appearing usually in Γ-limit functional of the rescaled p-compliance functional.doi:10.3934/nhm.2014.9.161 fatcat:2h2y2tgovjfanlxbvtcb3sfkh4