In
mathematics, a
Sobolev space is a
vector space of functions equipped with a
norm that is a combination of
L<sup>p</sup>-norms of the function itself and its derivatives up to a given order. The derivatives are understood in a suitable
weak sense to make the space
complete, thus a
Banach space. Intuitively, a Sobolev space is a space of functions with sufficiently many derivatives for some application domain, such as
partial differential equations, and equipped with a norm that measures both the size and regularity of a function.