Poincaré–Friedrichs inequality

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The Poincaré–Friedrichs inequality states that

C\int_G u^2 \, dx \leq \int_G \sum_{j=1}^N(\partial_j u)^2 \, dx \quad \forall u\in \overline{W}_2^1(G)

where \overline{W}_2^1 is a Sobolev space, the closure of the set C_0^\infty(G) in the Hilbert space W_2^1(G).

[edit] References

AMS 108 p. 136

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