Nonlinear Elliptic-Parabolic Equations with L1-data

This paper is devoted to the resolution of (P) (see below). No upper growth is assumed on g and ß is only locally lipschitz non decreasing function. This assumption on ß infers that the equation changes type. The method needs few non standard integration by parts and a compactness result due to the non linearity of a_ij:and g. Note also that the fact that the data are in L¹infers that u is not very regular.