Exploring Variational Functions - Calculus of Variations and Geometric Measure Theory

Explore the interface of Calculus of Variations and Geometric Measure Theory in this 48-minute presentation by Luigi Ambrosio from Scuola Normal Superiore, Pisa, Italy. Delve into second-order variational problems within bounded variation functions, analyzing extremality properties of continuous and piecewise affine functions in a unit ball energy context crucial for regularization in applied fields. Investigate a notable approximation theorem with piecewise affine functions, inspired by insights from the machine learning community. The presentation covers collaborative work with C. Brena, S. Conti, S. Aziznejad, and M. Unser, and includes a Q&A session. Gain valuable insights into the latest developments in the analysis of partial differential equations and their applications in mathematical modeling, applied mathematics, computational science, and data science.