Nonlinear Elliptic-Parabolic Equations with L¹-data

Abstract

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.

Keywords:

• Elliptic-parabolic equations
• integration by parts
• compactness result

AMS:

• 35A15
• 35J70
• 35K15