PDE. Lecture #31. Weak Solution to the Dirichlet Problem for Poisson’s Equation

In this lecture we discuss weak solutions to Dirichlet problems for Poisson's equation.
1:00 Problem with homogeneous boundary condition.
2:10 Proposition 1.
10:15 Definition of a weak solution for homogeneous case.
10:53 Existence-Uniqueness theorem for homogeneous case.
12:40 Proof of the theorem.
16:10 Remark on uniqueness.
17:47 Non-homogeneous problem.
18:52 Definition of weak solution for non-homogeneous case.
23:11 Existence-uniqueness theorem for non-homogeneous case.
The material is based on Lectures 28-30. The links are below

[chhumchhunny]

Please make more vedeos about weak solution of Neumann and Robin boundary condition. Thank you