This lecture covers density results in Sobolev spaces, focusing on the applications and implications of these results. The instructor discusses the concept of density results in LP(r) spaces, highlighting the importance of understanding the behavior of functions in these spaces. The lecture progresses to explain the proof techniques used to establish density results, providing insights into the extension of functions by zero outside a given region. The instructor also explores the implications of density results in practical scenarios, emphasizing the significance of these results in the context of partial differential equations.