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Lax-Milgram Theorem

Let $\phi$ be a bounded Coercive bilinear Functional on a Hilbert Space $H$. Then for every bounded linear Functional $f$ on $H$, there exists a unique $x_f\in H$ such that

f(x)=\phi(x, x_f)

for all $x\in H$.


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

Zeidler, E. Applied Functional Analysis: Applications to Mathematical Physics. New York: Springer-Verlag, 1995.

© 1996-9 Eric W. Weisstein