Friedrichs inequality

Friedrichs' inequality is a mathematical result that provides a way to estimate the size of a function based on its rate of change. Specifically, it states that when certain boundary conditions are met, the overall magnitude (or energy) of a function inside a domain can be controlled by the magnitude of its derivatives (how quickly it changes). This is useful in understanding the stability and behavior of solutions to differential equations, ensuring that if the function’s changes are small, then the function itself remains bounded and well-behaved within the given region.