Logo

Mathematical Sciences Research Institute

Home » Workshop » Schedules » A weaker notion of convexity for Lagrangians not depending solely on velocities and positions.

A weaker notion of convexity for Lagrangians not depending solely on velocities and positions.

Hamiltonian systems, from topology to applications through analysis II November 26, 2018 - November 30, 2018

November 30, 2018 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Wilfrid Gangbo (University of California, Los Angeles)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

16-Gangbo

Abstract

In dynamical systems, one often encounters actions A ≡ RΩLx, v(x)%dx which
depend only on v, the velocity of the system and on % the distribution of the particles. In
this case, it is well–understood that convexity of L(x, ·) is the right notion to study variational
problems. In this talk, we consider a weaker notion of convexity which seems appropriate
when the action depends on other quantities such as electro–magnetic fields. Thanks to the
introduction of a gauge, we will argue why our problem reduces to understanding the relaxation
of a functional defined on the set of differential forms (Joint work with B. Dacorogna).

Supplements
Asset no preview Notes 943 KB application/pdf Download
Video/Audio Files

16-Gangbo

H.264 Video 16-Gangbo.mp4 437 MB video/mp4 Download
Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture. The videos are sold at cost for $20USD (shipping included). Please Click Here to send an email to MSRI to purchase the DVD.

See more of our Streaming videos on our main VMath Videos page.