Functional inequalities

Functional inequalities are mathematical tools that relate different properties of functions, such as their size, smoothness, or variability. They provide bounds or estimates that connect how a function behaves in one aspect to another. For example, they can show that if a function doesn't change too rapidly, then its overall size must be controlled in a certain way. These inequalities are essential in analyzing solutions to equations, understanding stability, and studying how functions behave under various conditions in fields like analysis and partial differential equations.