Coercive Functional

A bilinear Functional $\phi$ on a normed Space $E$ is called coercive (or sometimes Elliptic) if there exists a Positive constant $K$ such that

$$\phi(x, x)\geq K\Vert x\Vert^2$$

for all $x\in E$.

See also Lax-Milgram Theorem

References

Debnath, L. and Mikusinski, P. Introduction to Hilbert Spaces with Applications. San Diego, CA: Academic Press, 1990.