Date:
Thu, 18/12/202512:10-13:55
Location:
Ross 70
Title: A brief introduction to Young measures
Abstract: One of the basic questions in the calculus of variations is the existence of minimizers for integral functionals. However, in many cases minimizers do not exist: the minimizing sequence must oscillate faster and faster on small amplitudes, but these oscillations vanish in the limit (think of sin(nx)/n→ 0). Around 1940, L.C. Young developed a finer notion of convergence of functions to deal with this problem; 50 years later, these "Young measures" reappeared as a tool to study new problems, e.g., if fi : Ω⊂ℝn → ℝn satisfies dist(∇ fi , SO(n)) → 0 in Lp, does fi converge to a single element in SO(n)?
In this introductory talk I'll introduce Young measures and their original motivation, answer the above question (spoiler: yes!), and, if time permits, discuss some new developments.
Abstract: One of the basic questions in the calculus of variations is the existence of minimizers for integral functionals. However, in many cases minimizers do not exist: the minimizing sequence must oscillate faster and faster on small amplitudes, but these oscillations vanish in the limit (think of sin(nx)/n→ 0). Around 1940, L.C. Young developed a finer notion of convergence of functions to deal with this problem; 50 years later, these "Young measures" reappeared as a tool to study new problems, e.g., if fi : Ω⊂ℝn → ℝn satisfies dist(∇ fi , SO(n)) → 0 in Lp, does fi converge to a single element in SO(n)?
In this introductory talk I'll introduce Young measures and their original motivation, answer the above question (spoiler: yes!), and, if time permits, discuss some new developments.