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Lagrange two hundred years later (Aula Dini, Palazzo Castelletto)

Lagrange and Carathéodory: the transversality condition at infinity

speaker: Ivar Ekeland (Université Paris Dauphine)

abstract: I will consider a variant of the classical Bolza problem in the calculus of variations, where the integral to be minimized ranges from \(t=0\) to \(t=\infty\). What are the boundary conditions that will supplement the Euler-Lagrange equations ? More precisely, what is the growth condition on the solution when \(t\) goes to \(\infty\) ? Economists know it as the "transversality condition at infinity", and use it as a matter of course, but the mathematical situation is far from clear. I will describe the problems with this approach and suggest instead the royal road of Caratheodory

timetable:
Wed 17 Apr, 11:00 - 12:00, Aula Dini
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