Scalar weak maximum principle
An initial value problem corresponding to this differential equation is a specification of for each .
The differential operator is said to satisfy the scalar weak maximum principle if whenever is a solution for which there are constants and such that for all , then for all .
In other words, any bounded set in which the range of lies also contains the image of for all .
Definition in terms of trajectory properties
Relation with other properties=
One-sided maximum principles
- The flow equation is said to satisfy a one-sided scalar weak maximum principle if the trajectories of the flow equation are only min-increasing