Well-Posedness of Elliptic PDEs

This lecture covers the concept of well-posedness of elliptic partial differential equations, focusing on various boundary conditions such as homogeneous Dirichlet conditions. The instructor explains the weak formulation of the Poisson equation and how to derive it. The lecture also discusses coercivity and the density of function spaces in the context of Poisson equations with homogeneous Dirichlet boundary conditions. Additionally, it explores the coercivity of the weak formulation and the uniqueness of solutions. The presentation concludes with examples illustrating the properties of linear and bounded operators in the context of elliptic PDEs.