ONE DIMENSIONAL MAXIMUM PRINCIPLE IN GEOMETRIC SETTING

Using a geometric setting of the one dimensional maximum principle, we introduce and study some classes of affine functions. Then we extend our study to differential inequalities which are of great interest in Mathematical Physics. Section 1 introduces the idea of maximum principle in geometrical language. Section 2 refreshes the one dimensional maximum principle theory. Section 3 gives the behavior of Γ-linear affine functions at the boundary. Section 4 analyzes important differential inequalities and Section 5 underlines new properties of special functions.