maximum principle

The maximum principle is a concept in mathematics, particularly in differential equations, that states: for certain "well-behaved" systems, the highest or lowest values of a solution occur on the boundary of the domain they are defined in. In other words, if you're solving a problem like heat distribution or electric potential, the maximum or minimum temperature or voltage inside the area can't be greater or smaller than those on its edge, unless the solution is constant. This principle helps ensure solutions behave predictably and helps in verifying the correctness of models.