Can anyone explain me the features of a compactly supported functions behave when they are compactly supported. I am learning PDE and I come across it very often.
For example : When we define weak derivatives i.e
$\int_U uD^\alpha f=(-1)^{|\alpha|}\int_U vf$ , why do we take a function $f$ to be compactly supported ?
I wonder if it is has to do with the non-differentiability of $u$ at some point in the domain ?
Looking forward. Thanks