Trudinger's theorem
In mathematical analysis, Trudinger's theorem or the Trudinger inequality is a result of functional analysis on Sobolev spaces. It is named after Neil Trudinger.
It provides an inequality between a certain Sobolev space norm and an Orlicz space norm of a function. The inequality is a limiting case of Sobolev imbedding and can be stated as the following theorem:
Let be a bounded domain in satisfying the cone condition. Let and. Set
Then there exists the embedding
where
The space
is an example of an Orlicz space.
