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Optimal rate of convergence in periodic homogenization of Hamilton-Jacobi equations

Hamiltonian systems, from topology to applications through analysis I October 08, 2018 - October 12, 2018

October 09, 2018 (09:15 AM PDT - 10:15 AM PDT)
Speaker(s): Yifeng Yu (University of California, Irvine)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Periodic homogenization

  • optimal convergence rate

  • Aubry-Mather theory

  • weak KAM theory

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Abstract

In this talk, I will present some recent progress in obtaining the optimal rate of convergence $O(\epsilon)$ in periodic homogenization of Hamilton-Jacobi equations. Our method is completely different from previous pure PDE approaches which only provides $O(\epsilon^{1/3})$. We have discovered a natural connection between the convergence rate and the underlying Hamiltonian system. This allows us to employ powerful tools from the Aubry-Mather theory and the weak KAM theory. It is a joint work with Hiroyashi Mitake and Hung V. Tran.

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