Non-compact Newton boundary and Whitney equisingularity for non-isolated singularities

In an unpublished lecture note, J. Briançon observed that if {ft} is a family of isolated complex hypersurface singularities such that the Newton boundary of ft is independent of t and ft is non-degenerate, then the corresponding family of hypersurfaces {ft−1(0)} is Whitney equisingular (and hence topologically equisingular). A first generalization of this assertion to families with non-isolated singularities was given by the second author under a rather technical condition. In the present paper, we give a new generalization under a simpler condition.