Arshak Petrosyan, Enrico Valdinoci Density estimates for a degenerate/singular phase-transition model (54K, LaTeX) ABSTRACT. We consider a Ginzburg-Landau type phase-transition model driven by a $p$-Laplacian type equation. We prove density estimates for absolute minimizers and we deduce the uniform convergence of level sets and the existence of plane-like minimizers in periodic media.