Sobolev space

Sobolev spaces are mathematical constructs used to analyze functions that have certain levels of smoothness, meaning they are differentiable in some sense. They help measure not just a function's values but also the behavior of its derivatives (rates of change), even if the derivatives aren't perfectly smooth. This makes Sobolev spaces a powerful tool in fields like partial differential equations and engineering, allowing us to handle functions that may be irregular or rough, yet still possess enough structure to study their properties and solutions systematically.