Lecture 6.4: Laplace equation - Weak maximum principle and its applications
Channel: IIT Bombay July 2018
Date: 2021-09-24

In this lecture, it is proved that harmonic functions in a bounded domain attain their maximum on the boundary. As a consequence, it is shown that solutions to Dirichlet problems depend continuously on boundary data. This provides us another way of proving uniqueness for Dirichlet boundary value problems for the Laplacian.