A two-phase problem with degenerate operator in Orlicz-Sobolev spaces

In this paper we are interested in the study of a two-phase problem equipped with the Φ-Laplacian operator Δ_Φ u div (φ(|∇ u|)∇ u/|∇ u|), where Φ(s)=es²-1 and φ=Φ'. We obtain the existence, boundedness, and Log-Lipschitz regularity of the minimizers of the energy functional associated to the two-phase problem. Furthermore, we also prove that the phase change free boundaries of the minimizers possess a finite perimeter.