JournalsifbVol. 11 , No. 2DOI 10.4171/ifb/208Flat free boundaries regularity in two-phase problems for a class of fully nonlinear elliptic operators with variable coefﬁcientsRoberto ArgiolasUniv. Studi Cagliari, ItalyFausto FerrariUniversità di Bologna, ItalyDownload PDFAbstractWe study the regularity of the free boundary in two-phase problems for fully nonlinear elliptic operators. In particular, we prove that ﬂat free boundaries are _C_1,γ.