In mathematics, Friedrichs's inequality is a theorem of functional analysis, due to Kurt Friedrichs.
It places a bound on the Lp norm of a function using Lp bounds on the weak derivatives of the function and the geometry of the domain, and can be used to show that certain norms on Sobolev spaces are equivalent.
Friedrichs's inequality generalizes the Poincaré–Wirtinger inequality, which deals with the case k = 1.
be a bounded subset of Euclidean space
with diameter
Suppose that
lies in the Sobolev space
and the trace of
on the boundary
α
α
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