Abstract :

In theoretical PDE, Lax-Milgram theorem is used to prove the existence of a weak solution of various PDE’s. The theorem guarantees the equality between certain bilinear form on a normed linear space V and the elements of V', the dual of V. In this talk we shall see a proof of the theorem using a consequence of Hahn- Banach extension theorem. Also, we will try to see some applications of the theorem.