Why the generalized derivatives defined? Why was it needed?

Question

While I was searching "why the generalized derivatives defined?", I saw the expression:

"An extension of the idea of a derivative to some classes of non-differentiable functions." on https://www.encyclopediaofmath.org/index.php/Generalized_derivative . But I need more knowledge about the emergence of the generalized derivative (or in the sense of Sobolev). Why this type derivatives defined? Why was it needed?

Can somebody recommend a source to me?

Answer 1

Here is a very interesting survey on the birth of Sobolev spaces: file