Lax-Milgram Theorem

FunctionalAnalysisPDEs The Lax-Milgram Theorem provides conditions when linear equations, , hold in a Hilbert Space in the folllowing sense: for all . It is said the equation holds in the weak sense. When , this is the Riesz-Representation Theorem, so that the theorem generalizes to the case where the RHS is not symmetric. The theorem states the following:

Given s.t. :

2. then for every , s.t.