Weak Formulation of Elliptic PDEs

This lecture covers the weak formulation of elliptic partial differential equations, including the Lax-Milgram theorem, homogeneous and non-homogeneous Dirichlet boundary conditions, Neumann boundary conditions, and the general and higher-order elliptic PDEs. The lecture also discusses the weak formulation in Hilbert space, the bilinear form, continuous and coercive properties, and the uniqueness of solutions. The presentation includes the continuous and coercive properties of the weak formulation, the Lax-Milgram theorem, and the uniqueness of solutions in Hilbert space.