Lax-Milgram: Variational Problems and Riesz's Theorem

This lecture covers the Lax-Milgram theorem, focusing on variational problems and Riesz's representation theorem. It explains the concept of well-posedness for second-order linear elliptic problems and the abstract variational problem. The instructor discusses the properties of Hilbert spaces, bilinear forms, and coercivity. The lecture concludes with the proof of the Lax-Milgram theorem and the closure of the range of a linear operator.