Weak derivative
Generalisation of the derivative of a function / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Weak derivative?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the Lp space .
![]() | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (May 2014) |
The method of integration by parts holds that for differentiable functions and
we have
A function u' being the weak derivative of u is essentially defined by the requirement that this equation must hold for all infinitely differentiable functions vanishing at the boundary points (
).