@UNPUBLISHED{publication1, title = "Optimal regularity for a two-phase free boundary problem ruled by the infinity Laplacian", author = "{ARA{\'{U}}JO, Dami{\~{a}}o J.} and {TEIXEIRA, Eduardo V.} and {URBANO, Jos{\'{e}} Miguel}", year = "2018-12-11", abstract = " In this paper we consider a non-variational two-phase free boundary problem ruled by the infinity Laplacian. Our main result states that normalized viscosity solutions in B1 are universally Lipschitz continuous in B1/2, which is the optimal regularity for the problem. We make a new use of the Ishii-Lions' method, which works as a surrogate for the lack of a monotonicity formula and is bound to be applicable in related problems. ", url = "http://www.mat.uc.pt/preprints/eng\_2018.html", note = "" }