Delve into an advanced lecture on Partial Differential Equations delivered by Professor Giovanni Bellettini. Explore complex mathematical concepts and theories related to PDEs over the course of 1 hour and 32 minutes. Gain insights into the intricacies of this fundamental area of mathematics, building upon previous knowledge and advancing understanding of differential equations. Engage with rigorous mathematical analysis and problem-solving techniques as presented by an expert in the field. Suitable for graduate-level mathematics students and researchers interested in deepening their comprehension of partial differential equations and their applications.