In mathematics, Friedrichs' 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.
Statement of the inequality
In the above
- denotes the Lp norm;
- α = (α1, ..., αn) is a multi-index with norm |α| = α1 + ... + αn;
- Dαu is the mixed partial derivative
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