Trudinger's theorem

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In mathematical analysis, Trudinger's theorem or the Trudinger inequality (also sometimes called the Moser–Trudinger inequality) is a result of functional analysis on Sobolev spaces. It is named after Neil Trudinger (and Jürgen Moser).

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 imbedding


The space

is an example of an Orlicz space.


  • Moser, J. (1971), "A Sharp form of an Inequality by N. Trudinger", Indiana Univ. Math., 20: 1077–1092 .
  • Trudinger, N. S. (1967), "On imbeddings into Orlicz spaces and some applications", J. Math. Mech., 17: 473–483 .