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Seminar Talk

Analysis and PDE

Speaker: Son Tu, Michigan State University
Title: Convergence Rate for 1D Quasi-Periodic Homogenization of Hamilton-Jacobi Equations
When: Wednesday, April 17, 4:15 PM - 5:05 PM
Where: C304 Wells Hall
Contact: Jun Kitagawa (jun@msu.edu)
Lions, Papanicolaou, and Varadhan pioneered the homogenization of Hamilton-Jacobi equations in the periodic setting during the 1980s. The rate of convergence has received a lot of attention in the last decades, culminating in the optimal rate (2022). However, if the environment is not periodic, the problem of the rate of convergence is not yet settled. In this presentation, we show that there is an algebraic rate for convex, coercive Hamiltonians with quasi-periodic potentials in 1D. The method relies on new quantitative ergodic estimates as well as a connection between the long-time average of characteristics with the regularity of the effective Hamiltonian.