Periodic Homogenization of Hamilton--Jacobi Equations for Infinite Systems of Indistinguishable Particles
Abstract: We consider periodic homogenization of Hamilton--Jacobi equations on \(L^2(I;\mathbb{R}^d)\), motivated by infinite systems of indistinguishable particles on the torus. Although the microscopic problem is genuinely infinite-dimensional, when the initial data depend only on the mean configuration, the homogenized solution is governed by a finite-dimensional effective equation.
We will first discuss qualitative homogenization and an \(O(\varepsilon^{1/3})\) convergence rate for general coercive, possibly nonconvex Hamiltonians. We will then explain how convexity allows one to obtain the optimal \(O(\varepsilon)\) rate. The proofs address the lack of local compactness through several mechanisms: a viscosity-solution framework using Stegall’s variational principle, a compact quotient space, a variational approach based on a mean-endpoint action metric, and an infinite-dimensional curve-surgery construction.
Event Type: Seminar. Research Area: Analysis and Differential Geometry. Location: MSC W301. Speaker Name: Seho Park. Speaker Institution: University of Wisconsin-Madison.
Friday, November 13, 2026, 11:00 AM – 12:00 PM.