Coercive bilinear form

Summary

A coercive bilinear form on a real Hilbert space is a bilinear form $a$ with $a(u, u) \ge \alpha \norm{u}^2$ for a fixed $\alpha > 0$. Coercivity is the key hypothesis of the Lax–Milgram theorem. It turns the weak form of many elliptic partial differential equations into a problem with exactly one solution.