Extension Theorems: Sobolev Spaces and Poincaré Inequality

This lecture covers extension theorems in the context of Sobolev spaces and Poincaré inequality, discussing how to extend functions from a bounded domain to a larger space. The slides present the mathematical details step by step, showing the process of extending functions and the conditions under which this extension is valid. The lecture emphasizes the importance of understanding Sobolev spaces and the Poincaré inequality in the context of partial differential equations. It also introduces the concept of extension generators and explores the properties of these generators in different dimensions.