“Trudinger's theorem”的意思、由来-开放百科全书

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Trudinger's theorem

释义

References

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 embedding

where

The space

is an example of an Orlicz space.

References

{{citation|last=Moser|first=J.|authorlink=Jürgen Moser|title=A Sharp form of an Inequality by N. Trudinger|journal=Indiana Univ. Math.|volume=20|year=1971|pages=1077–1092}}.
{{citation|last=Trudinger|first=N. S.|authorlink=Neil Trudinger|title=On imbeddings into Orlicz spaces and some applications|journal=J. Math. Mech. |volume=17|year=1967|pages=473–483}}.

3 : Sobolev spaces|Inequalities|Theorems in analysis

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